What is the Least Common Multiple of 189 and 202?
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 189 and 202 is 38178.
LCM(189,202) = 38178
Least Common Multiple of 189 and 202 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 189 and 202, than apply into the LCM equation.
GCF(189,202) = 1
LCM(189,202) = ( 189 × 202) / 1
LCM(189,202) = 38178 / 1
LCM(189,202) = 38178
Least Common Multiple (LCM) of 189 and 202 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 189 and 202. First we will calculate the prime factors of 189 and 202.
Prime Factorization of 189
Prime factors of 189 are 3, 7. Prime factorization of 189 in exponential form is:
189 = 33 × 71
Prime Factorization of 202
Prime factors of 202 are 2, 101. Prime factorization of 202 in exponential form is:
202 = 21 × 1011
Now multiplying the highest exponent prime factors to calculate the LCM of 189 and 202.
LCM(189,202) = 33 × 71 × 21 × 1011
LCM(189,202) = 38178
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