Question

find the Lcm and H
cf of the folowing integers by the prime factorisation method 12 , 15 and 21

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Answer 1

Answer:

SOLUTION :  

(i) GIVEN : 15, 12 and 21

The prime factors of 15, 12 and 21 are :

12 = 2 x 2 x 3 = 2² × 3¹

15 = 3 x 5 = 3¹ × 5¹

21 = 3 x 7 = 3¹ × 7¹

L.C.M of 12, 15 and 21 =2² × 3¹ × 5¹ × 7¹ =  2 x 2 x 3 x 5 x 7 =  420

L.C.M of 12, 15 and 21 = 420

[LCM of two or more numbers = product of the greatest power of each prime factor involved in the numbers, with highest power.]

H.C.F of 12, 15 and 21 = 3

[HCF(Highest Common Factor) of two or more numbers= Product of the smallest Power of each common prime factor involved in the numbers.]

Hence, H.C.F( 12, 15 and 21) = 3 & L.C.M (12, 15 and 21)  420.