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What is the Least Common Multiple of 1764 and 1768?

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 1764 and 1768 is 779688.

LCM(1764,1768) = 779688

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Least Common Multiple of 1764 and 1768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1764 and 1768, than apply into the LCM equation.

GCF(1764,1768) = 4
LCM(1764,1768) = ( 1764 × 1768) / 4
LCM(1764,1768) = 3118752 / 4
LCM(1764,1768) = 779688

Least Common Multiple (LCM) of 1764 and 1768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1764 and 1768. First we will calculate the prime factors of 1764 and 1768.

Prime Factorization of 1764

Prime factors of 1764 are 2, 3, 7. Prime factorization of 1764 in exponential form is:

1764 = 22 × 32 × 72

Prime Factorization of 1768

Prime factors of 1768 are 2, 13, 17. Prime factorization of 1768 in exponential form is:

1768 = 23 × 131 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 1764 and 1768.

LCM(1764,1768) = 23 × 32 × 72 × 131 × 171
LCM(1764,1768) = 779688