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What is the Least Common Multiple of 45 and 110?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 45 and 110 is 990.

LCM(45,110) = 990

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Least Common Multiple of 45 and 110 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45 and 110, than apply into the LCM equation.

GCF(45,110) = 5
LCM(45,110) = ( 45 × 110) / 5
LCM(45,110) = 4950 / 5
LCM(45,110) = 990

Least Common Multiple (LCM) of 45 and 110 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 110. First we will calculate the prime factors of 45 and 110.

Prime Factorization of 45

Prime factors of 45 are 3, 5. Prime factorization of 45 in exponential form is:

45 = 32 × 51

Prime Factorization of 110

Prime factors of 110 are 2, 5, 11. Prime factorization of 110 in exponential form is:

110 = 21 × 51 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 110.

LCM(45,110) = 32 × 51 × 21 × 111
LCM(45,110) = 990

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Guest 2021-01-24 05:51:28

This is very helpful for me

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