Least Common Multiple of 3680 and 3688

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3680 and 3688 the smallest integer that is 1696480 that is divisible by both numbers.

Least Common Multiple (LCM) of 3680 and 3688 is 1696480.

LCM(3680,3688) = 1696480

LCM of 3680 and 3688

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

LCM of:
and

Least Common Multiple of 3680 and 3688

LCM of 3680 and 3688 is 1696480

Least common multiple can be found by multiplying the highest exponent prime factors of 3680 and 3688. First we will calculate the prime factors of 3680 and 3688.

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

Prime Factorization of 3688


2 3688
2 1844
2 922
461 461
1

Prime factors of 3688 are 2,461. Prime factorization of 3688 in exponential form is:

3688 = 23×4611

Now multiplying the highest exponent prime factors to calculate the LCM of 3680 and 3688.

LCM(3680,3688) = 25×51×231×4611
LCM(3680,3688) = 1696480

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

Factors of 3688

List of positive integer factors of 3688 that divides 3688 without a remainder.

1, 2, 4, 8, 461, 922, 1844, 3688

Least Common Multiple of 3680 and 3688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3680 and 3688, than apply into the LCM equation.

GCF(3680,3688) = 8
LCM(3680,3688) = ( 3680 × 3688) / 8
LCM(3680,3688) = 13571840 / 8
LCM(3680,3688) = 1696480

Properties of LCM 3680 and 3688

(i) The LCM of 3688 and 3680 is associative

LCM of 3680 and 3688 = LCM of 3688 and 3680

Related Least Common Multiples of 3680

Related Least Common Multiples of 3688

Frequently Asked Questions on LCM of 3680 and 3688

1. What is the LCM of 3680 and 3688?

Answer: LCM of 3680 and 3688 is 1696480.

2. 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.

3. What are the Factors of 3688?

Answer: Factors of 3688 are 1, 2, 4, 8, 461, 922, 1844, 3688. There are 8 integers that are factors of 3688. The greatest factor of 3688 is 3688.

4. How to Find the LCM of 3680 and 3688?

Answer:

Least Common Multiple of 3680 and 3688 = 1696480

Step 1: Find the prime factorization of 3680

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

Step 2: Find the prime factorization of 3688

3688 = 2 x 2 x 2 x 461

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

LCM = 1696480 = 2 x 2 x 2 x 2 x 2 x 5 x 23 x 461

Step 4: Therefore, the least common multiple of 3680 and 3688 is 1696480.