What is the lcm of 25 and 15

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To get the Least Common Multiple (LCM) of 25 and 15 we need to factor each value first and then we choose all the factors which appear in any column and multiply them:

The Least Common Multiple (LCM) is:   3 x 5 x 5 = 75

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The lcm of 25 and 15 is the is the smallest positive integer that divides the numbers 25 and 15 without a remainder.Spelled out, it is the least common multiple of 25 and 15.

The least common multiple (LCM), the least common divisor (LCD), and the lowest common multiple (LCM) mean exactly the same. 🙂

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This Least Common Multiple Calculator is Really Cool! Click To TweetNote: Not only can our app determine the smallest common multiple of two, but also that of three or more integers including 25 and 15 for example.

Keep reading to learn all about the lcm / lcd of 25 and 15, including three methods for computing it.

What is the LCM of 25 and 15?

If you just want to know what’s the least common multiple of 25 and 15, it is 75.

Usually, this is written as

lcm(25,15) = 75
lcd(25,15) = 75

Next, we show you how to come up with this number by means of finding the largest integer which appears in both lists of multiples.

We also discuss how the greatest common factor, and the common list of primes with multiplicities can be used for that purpose.

How to Find the LCM of 25 and 15

Here’s how the number can be obtained using 3 methods:

Common Multiples Method

  • The multiples of 25 are 25, 50, 75, 100, 125, 150, …
  • The multiples of 15 are 15, 30, 45, 60, 75, 90, …
  • The common multiples of 25 and 15 are n × 75, intersecting the two sets above, n ∈ Z, n ≠ 0.
  • In the intersection multiples of 25 ∩ multiples of 15 the least positive element is 75.
  • Therefore, the least common multiple of 25 and 15 is 75.
Taking the above into account you also know how to find all the common multiples of 25 and 15, not just the least.On our home page you can find a link to our multiples calculator.

In the next section we show you how to calculate the lcm of twenty-five and fifteen by means of two more methods.

GCF Method

The least common multiple of 25 and 15 can be computed by using the greatest common factor aka gcf of 25 and 15.This is the easiest approach:

lcm (25,15) = 25 × 15 ⁄ gcf(25,15) = 375 ⁄ 5 = 75

Alternatively, the lcd of 25 and 15 can be found using the prime factorization of 25 and 15:

Prime Factors Method

  • The prime factorization of 25 is: 5 × 5, in exponent form: 52
  • The prime factorization of 15 is: 3 × 5, in exponential form: 31 × 51
  • Multiply the prime factors as many times as they occur most often:3 × 5 × 5 = 31 × 52 = lcm(25,15) = 75.
On our home page you can find a link to our prime factorization calculator as well as a link to our prime factors calculator.

How to Really Calculate the LCD of 25 and 15

In any case, the easiest way to find the lcm of two numbers like 25 and 15 is by using our lcm calculator at the top of this article.Note that it can also compute the lcm of more than two numbers, separated by a comma.For example, enter 25, 15, n; n ∈ N, n ≠ 0.The calculation is done automatically.

Similar searched terms on our site also include:

Use of LCM of 25 and 15

What is the least common multiple of 25 and 15 used for?Answer: It is helpful for adding and subtracting fractions like 1/25 and 1/15.

Just multiply the dividends and divisors by 3 and 5, respectively, such that the divisors have the value of 75, the lcm of 25 and 15.

Examples

1 ⁄ 25 + 1 ⁄ 15 = 3 ⁄ 75 + 5 ⁄ 75 = 8 ⁄ 75.

1 ⁄ 25 – 1 ⁄ 15 = 3 ⁄ 75 – 5 ⁄ 75 = -2 ⁄ 75.

Properties of LCM of 25 and 15

The most important properties of the lcm(25,15) are:
  • Commutative property: lcm(25,15) = lcm(15,25)
  • Associative property: lcm(25,15,n) = lcm(lcm(15,25),n) n ∈ N, n ≠ 0.
  • Distributive property: lcm(n25,n15) = n × lcm(15,25) n ∈ N, n ≠ 0
The associativity is particularly useful to get the lcm of three or more numbers; our gcd calculator makes use of it.

FAQs

A multiple of a number n is n, 2n, 3n, etc., n ∈ N, n ≠ 0. Thus, multiples of 25 are 25, 50, 75, 100, 125, 150, … . Multiples of 15 are 15, 30, 45, 60, 75, 90, … . The least common multiple of 25 and 15 is 75.

The factors of 25 = 1, 5, 25. The factors of 15 = 1, 3, 5, 15. Common factors of 25 and 15 = 1, 5.

The LCM of 25 and 15 = 75. The HCF (highest common factor) of 25 and 15 = 5.

The LCM of 25 and 15 = 75. The GCF of 25 and 15 = 5.

The prime factorization of 25 = 1 × 5 × 5. The prime factorization of 15 = 1 × 3 × 5.

Additional questions and comments are really appreciated!

Use the form below or send us a mail to get in touch about the mathematical concepts.

Summary

To sum up, the lcm of 25 and 15 is 75.We have shown you the detailed procedures for the listing multiples method, the prime factorization method as well as the greatest common method.On our home page you can find two more methods calculating the number, the division method and the cake method aka ladder method.

The latter algorithm is sometimes referred to as (factor) box method and as grid method.

What is the lcm of 25 and 15
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Table

The following table contains the lcm of three numbers: 25, 15 and n:

LCM(25,15,n)GCF(25,15,n)
lcm(25,15,1) = 75gcf(25,15,1) = 1
lcm(25,15,2) = 150gcf(25,15,2) = 1
lcm(25,15,3) = 75gcf(25,15,3) = 1
lcm(25,15,4) = 300gcf(25,15,4) = 1
lcm(25,15,5) = 75gcf(25,15,5) = 5
lcm(25,15,6) = 150gcf(25,15,6) = 1
lcm(25,15,7) = 525gcf(25,15,7) = 1
lcm(25,15,8) = 600gcf(25,15,8) = 1
lcm(25,15,9) = 225gcf(25,15,9) = 1
lcm(25,15,10) = 150gcf(25,15,10) = 5
lcm(25,15,11) = 825gcf(25,15,11) = 1
lcm(25,15,12) = 300gcf(25,15,12) = 1
lcm(25,15,13) = 975gcf(25,15,13) = 1
lcm(25,15,14) = 1050gcf(25,15,14) = 1
lcm(25,15,15) = 75gcf(25,15,15) = 5
lcm(25,15,16) = 1200gcf(25,15,16) = 1
lcm(25,15,17) = 1275gcf(25,15,17) = 1
lcm(25,15,18) = 450gcf(25,15,18) = 1
lcm(25,15,19) = 1425gcf(25,15,19) = 1
lcm(25,15,20) = 300gcf(25,15,20) = 5
lcm(25,15,21) = 525gcf(25,15,21) = 1
lcm(25,15,22) = 1650gcf(25,15,22) = 1
lcm(25,15,23) = 1725gcf(25,15,23) = 1
lcm(25,15,24) = 600gcf(25,15,24) = 1
lcm(25,15,25) = 75gcf(25,15,25) = 5
lcm(25,15,26) = 1950gcf(25,15,26) = 1
lcm(25,15,27) = 675gcf(25,15,27) = 1
lcm(25,15,28) = 2100gcf(25,15,28) = 1
lcm(25,15,29) = 2175gcf(25,15,29) = 1
lcm(25,15,30) = 150gcf(25,15,30) = 5
lcm(25,15,31) = 2325gcf(25,15,31) = 1
lcm(25,15,32) = 2400gcf(25,15,32) = 1
lcm(25,15,33) = 825gcf(25,15,33) = 1
lcm(25,15,34) = 2550gcf(25,15,34) = 1
lcm(25,15,35) = 525gcf(25,15,35) = 5
lcm(25,15,36) = 900gcf(25,15,36) = 1
lcm(25,15,37) = 2775gcf(25,15,37) = 1
lcm(25,15,38) = 2850gcf(25,15,38) = 1
lcm(25,15,39) = 975gcf(25,15,39) = 1
lcm(25,15,40) = 600gcf(25,15,40) = 5
lcm(25,15,41) = 3075gcf(25,15,41) = 1
lcm(25,15,42) = 1050gcf(25,15,42) = 1
lcm(25,15,43) = 3225gcf(25,15,43) = 1
lcm(25,15,44) = 3300gcf(25,15,44) = 1
lcm(25,15,45) = 225gcf(25,15,45) = 5
lcm(25,15,46) = 3450gcf(25,15,46) = 1
lcm(25,15,47) = 3525gcf(25,15,47) = 1
lcm(25,15,48) = 1200gcf(25,15,48) = 1
lcm(25,15,49) = 3675gcf(25,15,49) = 1
lcm(25,15,50) = 150gcf(25,15,50) = 5
lcm(25,15,51) = 1275gcf(25,15,51) = 1
lcm(25,15,52) = 3900gcf(25,15,52) = 1
lcm(25,15,53) = 3975gcf(25,15,53) = 1
lcm(25,15,54) = 1350gcf(25,15,54) = 1
lcm(25,15,55) = 825gcf(25,15,55) = 5
lcm(25,15,56) = 4200gcf(25,15,56) = 1
lcm(25,15,57) = 1425gcf(25,15,57) = 1
lcm(25,15,58) = 4350gcf(25,15,58) = 1
lcm(25,15,59) = 4425gcf(25,15,59) = 1
lcm(25,15,60) = 300gcf(25,15,60) = 5
lcm(25,15,61) = 4575gcf(25,15,61) = 1
lcm(25,15,62) = 4650gcf(25,15,62) = 1
lcm(25,15,63) = 1575gcf(25,15,63) = 1
lcm(25,15,64) = 4800gcf(25,15,64) = 1
lcm(25,15,65) = 975gcf(25,15,65) = 5
lcm(25,15,66) = 1650gcf(25,15,66) = 1
lcm(25,15,67) = 5025gcf(25,15,67) = 1
lcm(25,15,68) = 5100gcf(25,15,68) = 1
lcm(25,15,69) = 1725gcf(25,15,69) = 1
lcm(25,15,70) = 1050gcf(25,15,70) = 5
lcm(25,15,71) = 5325gcf(25,15,71) = 1
lcm(25,15,72) = 1800gcf(25,15,72) = 1
lcm(25,15,73) = 5475gcf(25,15,73) = 1
lcm(25,15,74) = 5550gcf(25,15,74) = 1
lcm(25,15,75) = 75gcf(25,15,75) = 5
lcm(25,15,76) = 5700gcf(25,15,76) = 1
lcm(25,15,77) = 5775gcf(25,15,77) = 1
lcm(25,15,78) = 1950gcf(25,15,78) = 1
lcm(25,15,79) = 5925gcf(25,15,79) = 1
lcm(25,15,80) = 1200gcf(25,15,80) = 5
lcm(25,15,81) = 2025gcf(25,15,81) = 1
lcm(25,15,82) = 6150gcf(25,15,82) = 1
lcm(25,15,83) = 6225gcf(25,15,83) = 1
lcm(25,15,84) = 2100gcf(25,15,84) = 1
lcm(25,15,85) = 1275gcf(25,15,85) = 5
lcm(25,15,86) = 6450gcf(25,15,86) = 1
lcm(25,15,87) = 2175gcf(25,15,87) = 1
lcm(25,15,88) = 6600gcf(25,15,88) = 1
lcm(25,15,89) = 6675gcf(25,15,89) = 1
lcm(25,15,90) = 450gcf(25,15,90) = 5
lcm(25,15,91) = 6825gcf(25,15,91) = 1
lcm(25,15,92) = 6900gcf(25,15,92) = 1
lcm(25,15,93) = 2325gcf(25,15,93) = 1
lcm(25,15,94) = 7050gcf(25,15,94) = 1
lcm(25,15,95) = 1425gcf(25,15,95) = 5
lcm(25,15,96) = 2400gcf(25,15,96) = 1
lcm(25,15,97) = 7275gcf(25,15,97) = 1
lcm(25,15,98) = 7350gcf(25,15,98) = 1
lcm(25,15,99) = 2475gcf(25,15,99) = 1
lcm(25,15,100) = 300gcf(25,15,100) = 5

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