Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 642 and 645 the smallest integer that is 138030 that is divisible by both numbers.
Least Common Multiple (LCM) of 642 and 645 is 138030.
LCM(642,645) = 138030
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 642 and 645. First we will calculate the prime factors of 642 and 645.
Prime Factorization of 642
2 | 642 |
3 | 321 |
107 | 107 |
1 |
Prime factors of 642 are 2, 3,107. Prime factorization of 642 in exponential form is:
642 = 21×31×1071
Prime Factorization of 645
3 | 645 |
5 | 215 |
43 | 43 |
1 |
Prime factors of 645 are 3, 5,43. Prime factorization of 645 in exponential form is:
645 = 31×51×431
Now multiplying the highest exponent prime factors to calculate the LCM of 642 and 645.
LCM(642,645) = 21×31×51×431×1071
LCM(642,645) = 138030
Factors of 642
List of positive integer factors of 642 that divides 642 without a remainder.
1, 2, 3, 6, 107, 214, 321, 642
Factors of 645
List of positive integer factors of 645 that divides 645 without a remainder.
1, 3, 5, 15, 43, 129, 215, 645
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 642 and 645, than apply into the LCM equation.
GCF(642,645) = 3
LCM(642,645) = ( 642 × 645) / 3
LCM(642,645) = 414090 / 3
LCM(642,645) = 138030
(i) The LCM of 645 and 642 is associative
LCM of 642 and 645 = LCM of 645 and 642
1. What is the LCM of 642 and 645?
Answer: LCM of 642 and 645 is 138030.
2. What are the Factors of 642?
Answer: Factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642. There are 8 integers that are factors of 642. The greatest factor of 642 is 642.
3. What are the Factors of 645?
Answer: Factors of 645 are 1, 3, 5, 15, 43, 129, 215, 645. There are 8 integers that are factors of 645. The greatest factor of 645 is 645.
4. How to Find the LCM of 642 and 645?
Answer:
Least Common Multiple of 642 and 645 = 138030
Step 1: Find the prime factorization of 642
642 = 2 x 3 x 107
Step 2: Find the prime factorization of 645
645 = 3 x 5 x 43
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 138030 = 2 x 3 x 5 x 43 x 107
Step 4: Therefore, the least common multiple of 642 and 645 is 138030.