Question

find the smallest number which when divided by 336, 54 and 108 using prime factorization method​

Answer 1

Step-by-step explanation:

Given numbers: 336 and 54

Let us find the prime factorisation of 336 & 54.

336 = 2×2×2×2×3×7

336 = 2⁴ × 3 × 7

54 = 2×3×3×3

54 = 2 × 3³

So,

HCF of (336, 54) = 2 × 3

HCF of (336, 54) = 6

LCM of (336, 54) = 2⁴ × 3 × 7

LCM of (336, 54) = 3024

Now consider

Multiples of HCF and LCm is equal to the product of two numbers.

HCF × LCM × HCF = Product of two numbers.

6 × 3024 = 336 × 54

18144 = 18144