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What is the Least Common Multiple of 7870 and 7890?

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 7870 and 7890 is 6209430.

LCM(7870,7890) = 6209430

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Least Common Multiple of 7870 and 7890 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7870 and 7890, than apply into the LCM equation.

GCF(7870,7890) = 10
LCM(7870,7890) = ( 7870 × 7890) / 10
LCM(7870,7890) = 62094300 / 10
LCM(7870,7890) = 6209430

Least Common Multiple (LCM) of 7870 and 7890 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7870 and 7890. First we will calculate the prime factors of 7870 and 7890.

Prime Factorization of 7870

Prime factors of 7870 are 2, 5, 787. Prime factorization of 7870 in exponential form is:

7870 = 21 × 51 × 7871

Prime Factorization of 7890

Prime factors of 7890 are 2, 3, 5, 263. Prime factorization of 7890 in exponential form is:

7890 = 21 × 31 × 51 × 2631

Now multiplying the highest exponent prime factors to calculate the LCM of 7870 and 7890.

LCM(7870,7890) = 21 × 51 × 7871 × 31 × 2631
LCM(7870,7890) = 6209430