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What is the Least Common Multiple of 1880 and 1890?

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 1880 and 1890 is 355320.

LCM(1880,1890) = 355320

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Least Common Multiple of 1880 and 1890 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1880 and 1890, than apply into the LCM equation.

GCF(1880,1890) = 10
LCM(1880,1890) = ( 1880 × 1890) / 10
LCM(1880,1890) = 3553200 / 10
LCM(1880,1890) = 355320

Least Common Multiple (LCM) of 1880 and 1890 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1880 and 1890. First we will calculate the prime factors of 1880 and 1890.

Prime Factorization of 1880

Prime factors of 1880 are 2, 5, 47. Prime factorization of 1880 in exponential form is:

1880 = 23 × 51 × 471

Prime Factorization of 1890

Prime factors of 1890 are 2, 3, 5, 7. Prime factorization of 1890 in exponential form is:

1890 = 21 × 33 × 51 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 1880 and 1890.

LCM(1880,1890) = 23 × 51 × 471 × 33 × 71
LCM(1880,1890) = 355320