Question

Find the hcf and lcm of 275, 225 and 175 by prime factorisation method

Answer 1

Answer:

HCF = 25

LCM = 17325

Step-by-step explanation:

275 = 5 * 5 * 11 * 1

225 = 3 * 3 * 5 * 5 * 1

175 = 5 * 5 * 7 * 1

Therefore HCF of 275, 225 and 175 is 5*5 = 25

LCM = 5 * 5 * 11 * 3 * 3 * 7 = 17325

Answer 2

Answer:

The factors of 175 are: 1, 5, 7, 25, 35, 175

The factors of 225 are: 1, 3, 5, 9, 15, 25, 45, 75, 225

The factors of 275 are: 1, 5, 11, 25, 55, 275

Then the highest common factor is 25.

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Prime Factorization of 175 is:

5 x 5 x 7  =>  5^2 x 7^1

Prime Factorization of 225 is:

3 x 3 x 5 x 5  =>  3^2 x 5^2

Prime Factorization of 275 is:

5 x 5 x 11  =>  5^2 x 11^1

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new list is

3, 3, 5, 5, 7, 11

Multiply these factors together to find the LCM.

LCM = 3 x 3 x 5 x 5 x 7 x 11 = 17325

In exponential form:

LCM = 3^2 x 5^2 x 7^1 x 11^1 = 17325

LCM = 17325

Therefore,

LCM(175, 225, 275) = 17,325

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