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What is the Least Common Multiple of 1600 and 1604?

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 1600 and 1604 is 641600.

LCM(1600,1604) = 641600

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Least Common Multiple of 1600 and 1604 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1600 and 1604, than apply into the LCM equation.

GCF(1600,1604) = 4
LCM(1600,1604) = ( 1600 × 1604) / 4
LCM(1600,1604) = 2566400 / 4
LCM(1600,1604) = 641600

Least Common Multiple (LCM) of 1600 and 1604 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1600 and 1604. First we will calculate the prime factors of 1600 and 1604.

Prime Factorization of 1600

Prime factors of 1600 are 2, 5. Prime factorization of 1600 in exponential form is:

1600 = 26 × 52

Prime Factorization of 1604

Prime factors of 1604 are 2, 401. Prime factorization of 1604 in exponential form is:

1604 = 22 × 4011

Now multiplying the highest exponent prime factors to calculate the LCM of 1600 and 1604.

LCM(1600,1604) = 26 × 52 × 4011
LCM(1600,1604) = 641600