Least Common Multiple of 3675 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 3675 and 3680 the smallest integer that is 2704800 that is divisible by both numbers.

Least Common Multiple (LCM) of 3675 and 3680 is 2704800.

LCM(3675,3680) = 2704800

LCM of 3675 and 3680

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

LCM of:
and

Least Common Multiple of 3675 and 3680

LCM of 3675 and 3680 is 2704800

Least common multiple can be found by multiplying the highest exponent prime factors of 3675 and 3680. First we will calculate the prime factors of 3675 and 3680.

Prime Factorization of 3675


3 3675
5 1225
5 245
7 49
7 7
1

Prime factors of 3675 are 3, 5,7. Prime factorization of 3675 in exponential form is:

3675 = 31×52×72

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 3675 and 3680.

LCM(3675,3680) = 25×31×52×72×231
LCM(3675,3680) = 2704800

Factors of 3675

List of positive integer factors of 3675 that divides 3675 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225, 3675

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 3675 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 3675 and 3680, than apply into the LCM equation.

GCF(3675,3680) = 5
LCM(3675,3680) = ( 3675 × 3680) / 5
LCM(3675,3680) = 13524000 / 5
LCM(3675,3680) = 2704800

Properties of LCM 3675 and 3680

(i) The LCM of 3680 and 3675 is associative

LCM of 3675 and 3680 = LCM of 3680 and 3675

Related Least Common Multiples of 3675

Related Least Common Multiples of 3680

Frequently Asked Questions on LCM of 3675 and 3680

1. What is the LCM of 3675 and 3680?

Answer: LCM of 3675 and 3680 is 2704800.

2. What are the Factors of 3675?

Answer: Factors of 3675 are 1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225, 3675. There are 18 integers that are factors of 3675. The greatest factor of 3675 is 3675.

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 3675 and 3680?

Answer:

Least Common Multiple of 3675 and 3680 = 2704800

Step 1: Find the prime factorization of 3675

3675 = 3 x 5 x 5 x 7 x 7

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 = 2704800 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 7 x 23

Step 4: Therefore, the least common multiple of 3675 and 3680 is 2704800.