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What is the Least Common Multiple of 1050 and 1070?

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 1050 and 1070 is 112350.

LCM(1050,1070) = 112350

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Least Common Multiple of 1050 and 1070 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1050 and 1070, than apply into the LCM equation.

GCF(1050,1070) = 10
LCM(1050,1070) = ( 1050 × 1070) / 10
LCM(1050,1070) = 1123500 / 10
LCM(1050,1070) = 112350

Least Common Multiple (LCM) of 1050 and 1070 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1050 and 1070. First we will calculate the prime factors of 1050 and 1070.

Prime Factorization of 1050

Prime factors of 1050 are 2, 3, 5, 7. Prime factorization of 1050 in exponential form is:

1050 = 21 × 31 × 52 × 71

Prime Factorization of 1070

Prime factors of 1070 are 2, 5, 107. Prime factorization of 1070 in exponential form is:

1070 = 21 × 51 × 1071

Now multiplying the highest exponent prime factors to calculate the LCM of 1050 and 1070.

LCM(1050,1070) = 21 × 31 × 52 × 71 × 1071
LCM(1050,1070) = 112350