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 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 Factorization of 1070

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