Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3674 and 3678 the smallest integer that is 6756486 that is divisible by both numbers.
Least Common Multiple (LCM) of 3674 and 3678 is 6756486.
LCM(3674,3678) = 6756486
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 3674 and 3678. First we will calculate the prime factors of 3674 and 3678.
Prime Factorization of 3674
2 | 3674 |
11 | 1837 |
167 | 167 |
1 |
Prime factors of 3674 are 2, 11,167. Prime factorization of 3674 in exponential form is:
3674 = 21×111×1671
Prime Factorization of 3678
2 | 3678 |
3 | 1839 |
613 | 613 |
1 |
Prime factors of 3678 are 2, 3,613. Prime factorization of 3678 in exponential form is:
3678 = 21×31×6131
Now multiplying the highest exponent prime factors to calculate the LCM of 3674 and 3678.
LCM(3674,3678) = 21×31×111×1671×6131
LCM(3674,3678) = 6756486
Factors of 3674
List of positive integer factors of 3674 that divides 3674 without a remainder.
1, 2, 11, 22, 167, 334, 1837, 3674
Factors of 3678
List of positive integer factors of 3678 that divides 3678 without a remainder.
1, 2, 3, 6, 613, 1226, 1839, 3678
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3674 and 3678, than apply into the LCM equation.
GCF(3674,3678) = 2
LCM(3674,3678) = ( 3674 × 3678) / 2
LCM(3674,3678) = 13512972 / 2
LCM(3674,3678) = 6756486
(i) The LCM of 3678 and 3674 is associative
LCM of 3674 and 3678 = LCM of 3678 and 3674
1. What is the LCM of 3674 and 3678?
Answer: LCM of 3674 and 3678 is 6756486.
2. What are the Factors of 3674?
Answer: Factors of 3674 are 1, 2, 11, 22, 167, 334, 1837, 3674. There are 8 integers that are factors of 3674. The greatest factor of 3674 is 3674.
3. What are the Factors of 3678?
Answer: Factors of 3678 are 1, 2, 3, 6, 613, 1226, 1839, 3678. There are 8 integers that are factors of 3678. The greatest factor of 3678 is 3678.
4. How to Find the LCM of 3674 and 3678?
Answer:
Least Common Multiple of 3674 and 3678 = 6756486
Step 1: Find the prime factorization of 3674
3674 = 2 x 11 x 167
Step 2: Find the prime factorization of 3678
3678 = 2 x 3 x 613
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6756486 = 2 x 3 x 11 x 167 x 613
Step 4: Therefore, the least common multiple of 3674 and 3678 is 6756486.