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What is the Least Common Multiple of 1635 and 1650?

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 1635 and 1650 is 179850.

LCM(1635,1650) = 179850

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Least Common Multiple of 1635 and 1650 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1635 and 1650, than apply into the LCM equation.

GCF(1635,1650) = 15
LCM(1635,1650) = ( 1635 × 1650) / 15
LCM(1635,1650) = 2697750 / 15
LCM(1635,1650) = 179850

Least Common Multiple (LCM) of 1635 and 1650 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1635 and 1650. First we will calculate the prime factors of 1635 and 1650.

Prime Factorization of 1635

Prime factors of 1635 are 3, 5, 109. Prime factorization of 1635 in exponential form is:

1635 = 31 × 51 × 1091

Prime Factorization of 1650

Prime factors of 1650 are 2, 3, 5, 11. Prime factorization of 1650 in exponential form is:

1650 = 21 × 31 × 52 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 1635 and 1650.

LCM(1635,1650) = 31 × 52 × 1091 × 21 × 111
LCM(1635,1650) = 179850