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What is the Least Common Multiple of 65940 and 65960?

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 65940 and 65960 is 217470120.

LCM(65940,65960) = 217470120

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Least Common Multiple of 65940 and 65960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65940 and 65960, than apply into the LCM equation.

GCF(65940,65960) = 20
LCM(65940,65960) = ( 65940 × 65960) / 20
LCM(65940,65960) = 4349402400 / 20
LCM(65940,65960) = 217470120

Least Common Multiple (LCM) of 65940 and 65960 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65940 and 65960. First we will calculate the prime factors of 65940 and 65960.

Prime Factorization of 65940

Prime factors of 65940 are 2, 3, 5, 7, 157. Prime factorization of 65940 in exponential form is:

65940 = 22 × 31 × 51 × 71 × 1571

Prime Factorization of 65960

Prime factors of 65960 are 2, 5, 17, 97. Prime factorization of 65960 in exponential form is:

65960 = 23 × 51 × 171 × 971

Now multiplying the highest exponent prime factors to calculate the LCM of 65940 and 65960.

LCM(65940,65960) = 23 × 31 × 51 × 71 × 1571 × 171 × 971
LCM(65940,65960) = 217470120