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What is the Least Common Multiple of 54774 and 54782?

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 54774 and 54782 is 1500314634.

LCM(54774,54782) = 1500314634

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Least Common Multiple of 54774 and 54782 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54774 and 54782, than apply into the LCM equation.

GCF(54774,54782) = 2
LCM(54774,54782) = ( 54774 × 54782) / 2
LCM(54774,54782) = 3000629268 / 2
LCM(54774,54782) = 1500314634

Least Common Multiple (LCM) of 54774 and 54782 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54774 and 54782. First we will calculate the prime factors of 54774 and 54782.

Prime Factorization of 54774

Prime factors of 54774 are 2, 3, 17, 179. Prime factorization of 54774 in exponential form is:

54774 = 21 × 32 × 171 × 1791

Prime Factorization of 54782

Prime factors of 54782 are 2, 7, 13, 43. Prime factorization of 54782 in exponential form is:

54782 = 21 × 72 × 131 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 54774 and 54782.

LCM(54774,54782) = 21 × 32 × 171 × 1791 × 72 × 131 × 431
LCM(54774,54782) = 1500314634