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What is the Least Common Multiple of 2120 and 2128?

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 2120 and 2128 is 563920.

LCM(2120,2128) = 563920

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Least Common Multiple of 2120 and 2128 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2120 and 2128, than apply into the LCM equation.

GCF(2120,2128) = 8
LCM(2120,2128) = ( 2120 × 2128) / 8
LCM(2120,2128) = 4511360 / 8
LCM(2120,2128) = 563920

Least Common Multiple (LCM) of 2120 and 2128 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2120 and 2128. First we will calculate the prime factors of 2120 and 2128.

Prime Factorization of 2120

Prime factors of 2120 are 2, 5, 53. Prime factorization of 2120 in exponential form is:

2120 = 23 × 51 × 531

Prime Factorization of 2128

Prime factors of 2128 are 2, 7, 19. Prime factorization of 2128 in exponential form is:

2128 = 24 × 71 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 2120 and 2128.

LCM(2120,2128) = 24 × 51 × 531 × 71 × 191
LCM(2120,2128) = 563920