Least Common Multiple of 2160 and 2164

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2160 and 2164 the smallest integer that is 1168560 that is divisible by both numbers.

Least Common Multiple (LCM) of 2160 and 2164 is 1168560.

LCM(2160,2164) = 1168560

LCM of 2160 and 2164

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

LCM of:
and

Least Common Multiple of 2160 and 2164

LCM of 2160 and 2164 is 1168560

Least common multiple can be found by multiplying the highest exponent prime factors of 2160 and 2164. First we will calculate the prime factors of 2160 and 2164.

Prime Factorization of 2160


2 2160
2 1080
2 540
2 270
3 135
3 45
3 15
5 5
1

Prime factors of 2160 are 2, 3,5. Prime factorization of 2160 in exponential form is:

2160 = 24×33×51

Prime Factorization of 2164


2 2164
2 1082
541 541
1

Prime factors of 2164 are 2,541. Prime factorization of 2164 in exponential form is:

2164 = 22×5411

Now multiplying the highest exponent prime factors to calculate the LCM of 2160 and 2164.

LCM(2160,2164) = 24×33×51×5411
LCM(2160,2164) = 1168560

Factors of 2160

List of positive integer factors of 2160 that divides 2160 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 90, 108, 120, 135, 144, 180, 216, 240, 270, 360, 432, 540, 720, 1080, 2160

Factors of 2164

List of positive integer factors of 2164 that divides 2164 without a remainder.

1, 2, 4, 541, 1082, 2164

Least Common Multiple of 2160 and 2164 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2160 and 2164, than apply into the LCM equation.

GCF(2160,2164) = 4
LCM(2160,2164) = ( 2160 × 2164) / 4
LCM(2160,2164) = 4674240 / 4
LCM(2160,2164) = 1168560

Properties of LCM 2160 and 2164

(i) The LCM of 2164 and 2160 is associative

LCM of 2160 and 2164 = LCM of 2164 and 2160

Related Least Common Multiples of 2160

Related Least Common Multiples of 2164

Frequently Asked Questions on LCM of 2160 and 2164

1. What is the LCM of 2160 and 2164?

Answer: LCM of 2160 and 2164 is 1168560.

2. What are the Factors of 2160?

Answer: Factors of 2160 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 90, 108, 120, 135, 144, 180, 216, 240, 270, 360, 432, 540, 720, 1080, 2160. There are 40 integers that are factors of 2160. The greatest factor of 2160 is 2160.

3. What are the Factors of 2164?

Answer: Factors of 2164 are 1, 2, 4, 541, 1082, 2164. There are 6 integers that are factors of 2164. The greatest factor of 2164 is 2164.

4. How to Find the LCM of 2160 and 2164?

Answer:

Least Common Multiple of 2160 and 2164 = 1168560

Step 1: Find the prime factorization of 2160

2160 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5

Step 2: Find the prime factorization of 2164

2164 = 2 x 2 x 541

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

LCM = 1168560 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 541

Step 4: Therefore, the least common multiple of 2160 and 2164 is 1168560.