Find LCM a , b and HCF a , b and verify that LCM a , b × HCF a , b = a b . For the following pair of integer a = 756 , b = 1044

Given, a = 756 , b = 1044 Prime factorization of the given pair of integer 756 = 2 × 2 × 3 × 3 × 3 × 7 1044 = 2 × 2 × 3 × 3 × 29 HCF of two numbers is the largest number that divides both of them. HCF 756 , 1044 = 2 × 2 × 3 × 3 = 36 For two integers a and b , denoted LCM ( a , b ) , the LCM is the smallest positive integer that is evenly divisible by both a and b . LCM 756 , 1044 = 2 × 2 × 3 × 3 × 3 × 7 × 29 = 21924 . From the properties of HCF and LCM, LCM ( a , b ) × HCF ( a , b ) = a × b ⇒ 21924 × 36 = 756 × 1044 ⇒ 789264 = 789264 Hence, LCM ( a , b ) × HCF ( a , b ) = a × b is verified

Find LCM a , b and HCF a , b and verify that LCM a , b × HCF a , b = a b . For the following pair of integer a = 756 , b = 1044

Given, a = 756 , b = 1044 Prime factorization of the given pair of integer 756 = 2 × 2 × 3 × 3 × 3 × 7 1044 = 2 × 2 × 3 × 3 × 29 HCF of two numbers is the largest number that divides both of them. HCF 756 , 1044 = 2 × 2 × 3 × 3 = 36 For two integers a and b , denoted LCM ( a , b ) , the LCM is the smallest positive integer that is evenly divisible by both a and b . LCM 756 , 1044 = 2 × 2 × 3 × 3 × 3 × 7 × 29 = 21924 . From the properties of HCF and LCM, LCM ( a , b ) × HCF ( a , b ) = a × b ⇒ 21924 × 36 = 756 × 1044 ⇒ 789264 = 789264 Hence, LCM ( a , b ) × HCF ( a , b ) = a × b is verified

Find LCM a , b and HCF a , b and verify that LCM a , b × HCF a , b = a b . For the following pair of integer a = 576 , b = 2520

Given, a = 576 , b = 2520 Prime factorization of the given pair of integer 576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 2520 = 2 × 2 × 2 × 3 × 3 × 5 × 7 HCF of two numbers is the largest number that divides both of them. HCF 576 , 2520 = 2 × 2 × 2 × 3 × 3 = 72 For two integers a and b , denoted LCM ( a , b ) , the LCM is the smallest positive integer that is evenly divisible by both a and b . LCM 576 , 2520 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 = 20160 . From the properties of HCF and LCM, LCM ( a , b ) × HCF ( a , b ) = a × b ⇒ 20160 × 72 = 576 × 2520 ⇒ 1451520 = 1451520 Hence, LCM ( a , b ) × HCF ( a , b ) = a × b is verified