Least Common Multiple of 2160 and 2167

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 2167 the smallest integer that is 4680720 that is divisible by both numbers.

Least Common Multiple (LCM) of 2160 and 2167 is 4680720.

LCM(2160,2167) = 4680720

LCM of 2160 and 2167

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

LCM of:
and

Least Common Multiple of 2160 and 2167

LCM of 2160 and 2167 is 4680720

Least common multiple can be found by multiplying the highest exponent prime factors of 2160 and 2167. First we will calculate the prime factors of 2160 and 2167.

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 2167


11 2167
197 197
1

Prime factors of 2167 are 11,197. Prime factorization of 2167 in exponential form is:

2167 = 111×1971

Now multiplying the highest exponent prime factors to calculate the LCM of 2160 and 2167.

LCM(2160,2167) = 24×33×51×111×1971
LCM(2160,2167) = 4680720

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 2167

List of positive integer factors of 2167 that divides 2167 without a remainder.

1, 11, 197, 2167

Least Common Multiple of 2160 and 2167 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 2167, than apply into the LCM equation.

GCF(2160,2167) = 1
LCM(2160,2167) = ( 2160 × 2167) / 1
LCM(2160,2167) = 4680720 / 1
LCM(2160,2167) = 4680720

Properties of LCM 2160 and 2167

(i) The LCM of 2167 and 2160 is associative

LCM of 2160 and 2167 = LCM of 2167 and 2160

Related Least Common Multiples of 2160

Related Least Common Multiples of 2167

Frequently Asked Questions on LCM of 2160 and 2167

1. What is the LCM of 2160 and 2167?

Answer: LCM of 2160 and 2167 is 4680720.

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 2167?

Answer: Factors of 2167 are 1, 11, 197, 2167. There are 4 integers that are factors of 2167. The greatest factor of 2167 is 2167.

4. How to Find the LCM of 2160 and 2167?

Answer:

Least Common Multiple of 2160 and 2167 = 4680720

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 2167

2167 = 11 x 197

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

LCM = 4680720 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 11 x 197

Step 4: Therefore, the least common multiple of 2160 and 2167 is 4680720.