What is the Least Common Multiple of 4185 and 4192?
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 4185 and 4192 is 17543520.
LCM(4185,4192) = 17543520
Least Common Multiple of 4185 and 4192 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4185 and 4192, than apply into the LCM equation.
GCF(4185,4192) = 1
LCM(4185,4192) = ( 4185 × 4192) / 1
LCM(4185,4192) = 17543520 / 1
LCM(4185,4192) = 17543520
Least Common Multiple (LCM) of 4185 and 4192 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 4185 and 4192. First we will calculate the prime factors of 4185 and 4192.
Prime Factorization of 4185
Prime factors of 4185 are 3, 5, 31. Prime factorization of 4185 in exponential form is:
4185 = 33 × 51 × 311
Prime Factorization of 4192
Prime factors of 4192 are 2, 131. Prime factorization of 4192 in exponential form is:
4192 = 25 × 1311
Now multiplying the highest exponent prime factors to calculate the LCM of 4185 and 4192.
LCM(4185,4192) = 33 × 51 × 311 × 25 × 1311
LCM(4185,4192) = 17543520
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