Question

what is the smallest natural number by which the following numbers should be multiplied so that they become perfect cube ? a)36 b)121 c)392​

Answer 1

Answer:

a) 6

b) 11

c) 7

this can be done by prime factorization

Answer 2

Answer:

a)36

lcm of 36 is 2×2×3×3

but we need one 2 and one 3 to form 36 a cube so we will multiply 2 and 3 it will give 6 and thus 6 is the smallest no to form 36 a perfect cube

36×6 =216 that is perfect cube

b)121

lcm of 121 is 11×11

but we need one more 11 to form 121 and cube so we will multiply 121 to 11 so it can form cube root

121×11 =1331 that is the perfect cube

c)392

lcm of 392 is 2×2×2×7×7

but we need one more 7 to form 392 a cube so we will multipy 7 to 392 to form it a perfect cube

392 ×7= 2744 that is a perfect cube

HOPE IT WILL HELP U✌✌