What is the Least Common Multiple of 57684 and 57693?
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 57684 and 57693 is 1109321004.
LCM(57684,57693) = 1109321004
Least Common Multiple of 57684 and 57693 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57684 and 57693, than apply into the LCM equation.
GCF(57684,57693) = 3
LCM(57684,57693) = ( 57684 × 57693) / 3
LCM(57684,57693) = 3327963012 / 3
LCM(57684,57693) = 1109321004
Least Common Multiple (LCM) of 57684 and 57693 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 57684 and 57693. First we will calculate the prime factors of 57684 and 57693.
Prime Factorization of 57684
Prime factors of 57684 are 2, 3, 11, 19, 23. Prime factorization of 57684 in exponential form is:
57684 = 22 × 31 × 111 × 191 × 231
Prime Factorization of 57693
Prime factors of 57693 are 3, 19231. Prime factorization of 57693 in exponential form is:
57693 = 31 × 192311
Now multiplying the highest exponent prime factors to calculate the LCM of 57684 and 57693.
LCM(57684,57693) = 22 × 31 × 111 × 191 × 231 × 192311
LCM(57684,57693) = 1109321004
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