Question

Find the LCM and HCF of the following integers by applying the prime factorization method
12,15 and 25

Answer 1

Hint: First we will find the prime factors of the 12,15 and 25. Then for LCM we will find the value of the common multiple of integers and for HCF we will find the highest common factors in integers.

Complete step-by-step answer:
Factorization of integers
$12 = 1 \times 2 \times 2 \times 3$
$15 = 1 \times 3 \times 5$
$25 = 1 \times 5 \times 5$
Now for LCM we have to find the common multiple of integers
 Common multiples of integers=$1 \times 2 \times 2 \times 3 \times 5 \times 5$
$\therefore LCM = 300$
Now for HCF we have to find highest common factor of the given integers
So, common factor is = 1
$\therefore HCF = 1$

Note: Full form of LCM and HCF are lowest common multiple and highest common factor respectively. LCM is defined as the least no. which is exactly divisible by given numbers it is also known as least common divisor, whereas HCF is defined as the greatest factor present in between the given two or more numbers. It is also known as the greatest common factor.