hcf of 2 numbers equal to the highest of all the common factors of the two numbers 23 is the common factor of the two numbers Let 23 x ,23 Y be the two numbers we know that the factor of any two numbers is also a factor of the LCM of that two numbers So 23 is a factor of the two numbers 23 x and 23 y LCM of two numbers 23 x and 23 Y = 13× 14 ×23 LCM =13×14 ×23 And HCF = 23 We know that , LCM× HCF = product of the two numbers 13 ×14 × 23 =23 x × 23 y @x×y= 13× 14 Which shows that larger number will be 14 ×23 that is equal to 322 Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now
India's Super Teachers for all govt. exams Under One Roof
Given: H.C.F. = 17 Two factors = 15 and 19 Concept used: Factors and Multiples: If number a divided another number b exactly, we say that a is a factor of b.While, b is called a multiple of a. The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly. The least number which is exactly divisible by each one of the given numbers is called their L.C.M. Product of two numbers = Product of their H.C.F. and L.C.M. Calculations: ⇒ Numbers = (17 × 15) and (17 × 19) ⇒ Numbers = 255 and 323 ⇒ Largest number = 323. ∴ The largest number is 323. India’s #1 Learning Platform Start Complete Exam Preparation
Daily Live MasterClasses
Practice Question Bank
Mock Tests & Quizzes Trusted by 3,09,38,385+ Students
We will learn the relationship between H.C.F. and L.C.M. of
two numbers. First we need to find the highest common factor (H.C.F.) of 15 and 18 which is 3. Then we need to find the lowest common multiple (L.C.M.) of 15 and 18 which is 90. H.C.F. × L.C.M. = 3 × 90 = 270 Also the product of numbers = 15 × 18 = 270 Therefore, product of H.C.F. and L.C.M. of 15 and 18 = product of 15 and 18. Again, let us consider the two numbers 16 and 24 Prime factors of 16 and 24 are: 16 = 2 × 2 × 2 × 2 24 = 2 × 2 × 2 × 3 L.C.M. of 16 and 24 is 48; H.C.F. of 16 and 24 is 8; L.C.M. × H.C.F. = 48 × 8 = 384 Product of numbers = 16 × 24 = 384 So, from the above explanations we conclude that the product of highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of two numbers is equal to the product of two numbers or, H.C.F. × L.C.M. = First number × Second number or, L.C.M. = \(\frac{\textrm{First Number} \times \textrm{Second Number}}{\textrm{H.C.F.}}\) or, L.C.M. × H.C.F. = Product of two given numbers or, L.C.M. = \(\frac{\textrm{Product of Two Given Numbers}}{\textrm{H.C.F.}}\) or, H.C.F. = \(\frac{\textrm{Product of Two Given Numbers}}{\textrm{L.C.M.}}\) Solved examples on the
relationship between H.C.F. and L.C.M.: 1. Find the L.C.M. of 1683 and 1584. Solution: First we find highest common factor of 1683 and 1584 Therefore, highest common factor of 1683 and 1584 = 99 Lowest common multiple of 1683 and 1584 = First number × Second number/ H.C.F. = \(\frac{1584 × 1683}{99}\) = 26928 2. Highest common factor and lowest common multiple of two numbers are 18 and 1782 respectively. One number is 162, find the other. Solution: We know, H.C.F. × L.C.M. = First number × Second number then we get, 18 × 1782 = 162 × Second number \(\frac{18 × 1782}{162}\) = Second number Therefore, the second number = 198 3. The HCF of two numbers is 3 and their LCM is 54. If one of the numbers is 27, find the other number. Solution: HCF × LCM = Product of two numbers 3 × 54 = 27 × second number Second number = \(\frac{3 × 54}{27}\) Second number = 6 4. The highest common factor and the lowest common multiple of two numbers are 825 and 25 respectively. If one of the two numbers is 275, find the other number. Solution: We know, H.C.F. × L.C.M. = First number × Second number then we get, 825 × 25 = 275 × Second number \(\frac{825 × 25}{275}\) = Second number Therefore, the second number = 75 5. Find the H.C.F. and L.C.M. of 36 and 48. Solution:
Therefore, product of the two numbers = H.C.F × L.C.M. 2. The H.C.F. of two numbers 30 and 42 is 6. Find the L.C.M. Solution: We have H.C.F. × L.C.M. = product of the numbers 6 × L.C.M. = 30 × 42 L.C.M. = \[\frac{30 × 42}{\sqrt{6}}\] = \[\frac{1260}{\sqrt{6}}\] = 210 3. Find the greatest number which divides 105 and 180 completely. Solution:
Therefore, the greatest number that divides 105 and 180 completely is 15. 4. Find the least number which leaves 3 as remainder when divided by 24 and 42. Solution:
The least number which leaves 3 as remainder is 168 + 3 = 171. Important Notes: Two numbers which have only 1 as the common factor are called co-prime. The least common multiple (L.C.M.) of two or more numbers is the smallest number which is divisible by all the numbers. If two numbers are co-prime, their L.C.M. is the product of the numbers. If one number is the multiple of the other, then the multiple is their L.C.M. L.C.M. of two or more numbers cannot be less than any one of the given numbers. H.C.F. of two or more numbers is the highest number that can divide the numbers without leaving any remainder. If one number is a factor of the second number then the smaller number is the H.C.F. of the two given numbers. The product of L.C.M. and H.C.F. of two numbers is equal to the product of the two given numbers. Questions and Answers on Relationship between H.C.F. and L.C.M. 1. The H.C.F. of two numbers 20 and 75 is 5. Find their L.C.M. 2. The L.C.M. of two numbers 72 and 180 is 360. Find their H.C.F. 3. The L.C.M. of two numbers is 120. If the product of the numbers is 1440, find the H.C.F. 4. Find the least number which leaves 5 as remainder when divided by 36 and 54. 5. The product of two numbers is 384. If their H.C.F. is 8, find the L.C.M. Answer: 1. 300 2. 36 3. 12 4. 113 5. 48
Common Multiples. Least Common Multiple (L.C.M). To find Least Common Multiple by using Prime Factorization Method. Examples to find Least Common Multiple by using Prime Factorization Method. To Find Lowest Common Multiple by using Division Method Examples to find Least Common Multiple of two numbers by using Division Method Examples to find Least Common Multiple of three numbers by using Division Method Relationship between H.C.F. and L.C.M. Worksheet on H.C.F. and L.C.M. Word problems on H.C.F. and L.C.M. Worksheet on word problems on H.C.F. and L.C.M. 5th Grade Math Problems From Relationship between H.C.F. and L.C.M. to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
|