Question

find LCM and HCF of the following number using prime factorization method? 765,510,408​

Answer 1

Example 1:

Find the LCM of 20 and 12 by prime factorization method.

Solution:

Step 1: To find LCM of 20 and 12, write each number as a product of prime factors.

20=2×2×5=22×512=2×2×3=22×3

Step 2: Multiply all the prime factors with the highest degree.

Here we have 2 with highest power 2 and other prime factors 3 and 5. Multiply all these to get LCM.

LCM of 20 and 12 = 2×2×3×5=22×3×5=60

LCM by Division Method

In this method, divide the given numbers by common prime number until the remainder is a prime number or one. LCM will be the product obtained by multiplying all divisors and remaining prime numbers.

Example 2:

Find the LCM of 24 and 15 by the division method.

Solution:

Step 1: Divide the given numbers by the least prime number.

Here, 2 is the least number which will divide 24.