Question

find the lcm and hcf of the following integers by applying the prime factorization method. 175 ,135 and 45​

Answer 1

Answer:

We can find HCF and LCM of given natural numbers by two methods i.e., by prime factorization method or division method. In the prime factorization method, given numbers are written as the product of prime factors. While in the division method, given numbers are divided by the least common factor and continue still remainder is zero.

Note: Prime numbers are numbers which have only two factors i.e. one and the number itself.

LCM by Prime Factorization Method

Here, given natural numbers are written as the product of prime factors. The lowest common multiple will be the product of all prime factors with the highest degree (power).

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

Step-by-step explanation:

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