Least Common Multiple of 3678 and 3680

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3678 and 3680 the smallest integer that is 6767520 that is divisible by both numbers.

Least Common Multiple (LCM) of 3678 and 3680 is 6767520.

LCM(3678,3680) = 6767520

LCM of 3678 and 3680

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 3678 and 3680

LCM of 3678 and 3680 is 6767520

Least common multiple can be found by multiplying the highest exponent prime factors of 3678 and 3680. First we will calculate the prime factors of 3678 and 3680.

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

Prime Factorization of 3680


2 3680
2 1840
2 920
2 460
2 230
5 115
23 23
1

Prime factors of 3680 are 2, 5,23. Prime factorization of 3680 in exponential form is:

3680 = 25×51×231

Now multiplying the highest exponent prime factors to calculate the LCM of 3678 and 3680.

LCM(3678,3680) = 25×31×51×231×6131
LCM(3678,3680) = 6767520

Factors of 3678

List of positive integer factors of 3678 that divides 3678 without a remainder.

1, 2, 3, 6, 613, 1226, 1839, 3678

Factors of 3680

List of positive integer factors of 3680 that divides 3680 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 80, 92, 115, 160, 184, 230, 368, 460, 736, 920, 1840, 3680

Least Common Multiple of 3678 and 3680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3678 and 3680, than apply into the LCM equation.

GCF(3678,3680) = 2
LCM(3678,3680) = ( 3678 × 3680) / 2
LCM(3678,3680) = 13535040 / 2
LCM(3678,3680) = 6767520

Properties of LCM 3678 and 3680

(i) The LCM of 3680 and 3678 is associative

LCM of 3678 and 3680 = LCM of 3680 and 3678

Related Least Common Multiples of 3678

Related Least Common Multiples of 3680

Frequently Asked Questions on LCM of 3678 and 3680

1. What is the LCM of 3678 and 3680?

Answer: LCM of 3678 and 3680 is 6767520.

2. 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.

3. What are the Factors of 3680?

Answer: Factors of 3680 are 1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 80, 92, 115, 160, 184, 230, 368, 460, 736, 920, 1840, 3680. There are 24 integers that are factors of 3680. The greatest factor of 3680 is 3680.

4. How to Find the LCM of 3678 and 3680?

Answer:

Least Common Multiple of 3678 and 3680 = 6767520

Step 1: Find the prime factorization of 3678

3678 = 2 x 3 x 613

Step 2: Find the prime factorization of 3680

3680 = 2 x 2 x 2 x 2 x 2 x 5 x 23

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 6767520 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 23 x 613

Step 4: Therefore, the least common multiple of 3678 and 3680 is 6767520.