Question

3. Find the LCM and HCF of the following integers by applying the prime factorisation
method
12, 15 and 21 ​

Answer 1

$\bf\purple{QuestioN:-}$

Find the LCM and HCF of the following integers by applying the prime factorisation method  12, 15 and 21 ​.

$\bf\red{AnsweR:-}$

We need to find LCM & HCF of 12, 15 and 21 by prime factorization method.

First we need to find the prime factors of the following numbers.

$\pink:\implies\pmb{12=2\times2\times3}$

$\pink:\implies\pmb{15=5\times3}$

$\pink:\implies\pmb{21=7\times3}$

LCM = 2 × 2 × 3 × 5 × 7

       = 420

HCF =  3

Verification:-

420 is divisible by 12, 15 and 21.

$\blue\longrightarrow\bf{\dfrac{420}{12}=35}$

$\blue\longrightarrow\bf{\dfrac{420}{15}=28}$

$\blue\longrightarrow\bf{\dfrac{420}{21}=20}$

Hence 420 is the Least Common Multiple of these numbers, ie, LCM.

No other number other than 3 is a common dividend of these numbers,

So 3 is the HCF or Highest Common Factor of these numbers.

Happy Learning!!♥