Question

lcm and hcf by the prime factorization of 12,15 and 21

Answer 1

12= 2×2×3
15=3×5
21=3×7
so,HCF of 12,15,21 = 3
LCM of 12,15,21 = 3×2×2×5×7 =420

Answer 2

Answer:

LCM (12, 15 and 21) =420

HCF (12, 15 and 21) =3

To find:

The LCM and HCF of the given numbers 12, 15 and 21

Solution:

The prime factors for 12, 15 and 25 are given as below

$\begin{aligned} 12 & = 2 \times 2 \times 3 \\\\ 12 & = 2 ^ { 2 } \times 3 ^ { 1 } \\\\ 15 & = 3 \times 5 \\\\ 15 & = 3 ^ { 1 } \times 5 ^ { 1 } \\\\ 21 & = 3 \times 7 \\\\ 21 & = 3 ^ { 1 } \times 7 ^ { 1 } \end{aligned}$

[For LCM, we need to take all the terms and for HCF only the common terms are taken into account]

$\begin{aligned} \text{ LCM } ( 12,15 \text { and } 21 ) & = 2 ^ { 2 } \times 3 \times 5 \times 7 \\\\ \text{ LCM } ( 12,15 \text { and } 21 ) & = 4 \times 3 \times 5 \times 7 \\\\ \text{ LCM } ( 12,15 \text { and } 21 ) & = 420 \\\\ \text { HCF } ( 12,15 \text { and } 21 ) & = 3 ^ { 1 } \\\\ \text{ HCF } ( 12,15 \text { and } 21 ) & = 3 \end{aligned}$