Question

Find the HCF of 44 and 444 by the prime factorization method hence, find their LCM

Answer 1

Answer:

HCF = 4

LCM = 4884

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Step-by-step explanation:

HCF

Answer:

HCF = 4

for the values 44, 444

Solution by Factorization:

The factors of 44 are: 1, 2, 4, 11, 22, 44

The factors of 444 are: 1, 2, 3, 4, 6, 12, 37, 74, 111, 148, 222, 444

Then the greatest common factor is 4.

LCM

Answer:

LCM = 4884

Solution by Prime Factorization

List all prime factors for each number.

Prime Factorization of 44 is:

2 x 2 x 11 => 2^2 x 11^1

Prime Factorization of 444 is:

2 x 2 x 3 x 37 => 2^2 x 3^1 x 37^1

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 superset list is

2, 2, 3, 11, 37

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 11 x 37 = 4884

In exponential form:

LCM = 2^2 x 3^1 x 11^1 x 37^1 = 4884

LCM = 4884

Therefore,

LCM(44, 444) = 4884

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