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What is the Least Common Multiple of 1965 and 1976?

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 1965 and 1976 is 3882840.

LCM(1965,1976) = 3882840

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Least Common Multiple of 1965 and 1976 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1965 and 1976, than apply into the LCM equation.

GCF(1965,1976) = 1
LCM(1965,1976) = ( 1965 × 1976) / 1
LCM(1965,1976) = 3882840 / 1
LCM(1965,1976) = 3882840

Least Common Multiple (LCM) of 1965 and 1976 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1965 and 1976. First we will calculate the prime factors of 1965 and 1976.

Prime Factorization of 1965

Prime factors of 1965 are 3, 5, 131. Prime factorization of 1965 in exponential form is:

1965 = 31 × 51 × 1311

Prime Factorization of 1976

Prime factors of 1976 are 2, 13, 19. Prime factorization of 1976 in exponential form is:

1976 = 23 × 131 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 1965 and 1976.

LCM(1965,1976) = 31 × 51 × 1311 × 23 × 131 × 191
LCM(1965,1976) = 3882840