Least Common Multiple of 2064 and 2070

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2064 and 2070 the smallest integer that is 712080 that is divisible by both numbers.

Least Common Multiple (LCM) of 2064 and 2070 is 712080.

LCM(2064,2070) = 712080

LCM of 2064 and 2070

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

LCM of:
and

Least Common Multiple of 2064 and 2070

LCM of 2064 and 2070 is 712080

Least common multiple can be found by multiplying the highest exponent prime factors of 2064 and 2070. First we will calculate the prime factors of 2064 and 2070.

Prime Factorization of 2064


2 2064
2 1032
2 516
2 258
3 129
43 43
1

Prime factors of 2064 are 2, 3,43. Prime factorization of 2064 in exponential form is:

2064 = 24×31×431

Prime Factorization of 2070


2 2070
3 1035
3 345
5 115
23 23
1

Prime factors of 2070 are 2, 3, 5,23. Prime factorization of 2070 in exponential form is:

2070 = 21×32×51×231

Now multiplying the highest exponent prime factors to calculate the LCM of 2064 and 2070.

LCM(2064,2070) = 24×32×51×231×431
LCM(2064,2070) = 712080

Factors of 2064

List of positive integer factors of 2064 that divides 2064 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 43, 48, 86, 129, 172, 258, 344, 516, 688, 1032, 2064

Factors of 2070

List of positive integer factors of 2070 that divides 2070 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 23, 30, 45, 46, 69, 90, 115, 138, 207, 230, 345, 414, 690, 1035, 2070

Least Common Multiple of 2064 and 2070 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2064 and 2070, than apply into the LCM equation.

GCF(2064,2070) = 6
LCM(2064,2070) = ( 2064 × 2070) / 6
LCM(2064,2070) = 4272480 / 6
LCM(2064,2070) = 712080

Properties of LCM 2064 and 2070

(i) The LCM of 2070 and 2064 is associative

LCM of 2064 and 2070 = LCM of 2070 and 2064

Related Least Common Multiples of 2064

Related Least Common Multiples of 2070

Frequently Asked Questions on LCM of 2064 and 2070

1. What is the LCM of 2064 and 2070?

Answer: LCM of 2064 and 2070 is 712080.

2. What are the Factors of 2064?

Answer: Factors of 2064 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 43, 48, 86, 129, 172, 258, 344, 516, 688, 1032, 2064. There are 20 integers that are factors of 2064. The greatest factor of 2064 is 2064.

3. What are the Factors of 2070?

Answer: Factors of 2070 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 23, 30, 45, 46, 69, 90, 115, 138, 207, 230, 345, 414, 690, 1035, 2070. There are 24 integers that are factors of 2070. The greatest factor of 2070 is 2070.

4. How to Find the LCM of 2064 and 2070?

Answer:

Least Common Multiple of 2064 and 2070 = 712080

Step 1: Find the prime factorization of 2064

2064 = 2 x 2 x 2 x 2 x 3 x 43

Step 2: Find the prime factorization of 2070

2070 = 2 x 3 x 3 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 = 712080 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 23 x 43

Step 4: Therefore, the least common multiple of 2064 and 2070 is 712080.