Least Common Multiple of 1656 and 1664

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1656 and 1664 the smallest integer that is 344448 that is divisible by both numbers.

Least Common Multiple (LCM) of 1656 and 1664 is 344448.

LCM(1656,1664) = 344448

LCM of 1656 and 1664

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

LCM of:
and

Least Common Multiple of 1656 and 1664

LCM of 1656 and 1664 is 344448

Least common multiple can be found by multiplying the highest exponent prime factors of 1656 and 1664. First we will calculate the prime factors of 1656 and 1664.

Prime Factorization of 1656


2 1656
2 828
2 414
3 207
3 69
23 23
1

Prime factors of 1656 are 2, 3,23. Prime factorization of 1656 in exponential form is:

1656 = 23×32×231

Prime Factorization of 1664


2 1664
2 832
2 416
2 208
2 104
2 52
2 26
13 13
1

Prime factors of 1664 are 2,13. Prime factorization of 1664 in exponential form is:

1664 = 27×131

Now multiplying the highest exponent prime factors to calculate the LCM of 1656 and 1664.

LCM(1656,1664) = 27×32×131×231
LCM(1656,1664) = 344448

Factors of 1656

List of positive integer factors of 1656 that divides 1656 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 69, 72, 92, 138, 184, 207, 276, 414, 552, 828, 1656

Factors of 1664

List of positive integer factors of 1664 that divides 1664 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664

Least Common Multiple of 1656 and 1664 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1656 and 1664, than apply into the LCM equation.

GCF(1656,1664) = 8
LCM(1656,1664) = ( 1656 × 1664) / 8
LCM(1656,1664) = 2755584 / 8
LCM(1656,1664) = 344448

Properties of LCM 1656 and 1664

(i) The LCM of 1664 and 1656 is associative

LCM of 1656 and 1664 = LCM of 1664 and 1656

Related Least Common Multiples of 1656

Related Least Common Multiples of 1664

Frequently Asked Questions on LCM of 1656 and 1664

1. What is the LCM of 1656 and 1664?

Answer: LCM of 1656 and 1664 is 344448.

2. What are the Factors of 1656?

Answer: Factors of 1656 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 69, 72, 92, 138, 184, 207, 276, 414, 552, 828, 1656. There are 24 integers that are factors of 1656. The greatest factor of 1656 is 1656.

3. What are the Factors of 1664?

Answer: Factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664. There are 16 integers that are factors of 1664. The greatest factor of 1664 is 1664.

4. How to Find the LCM of 1656 and 1664?

Answer:

Least Common Multiple of 1656 and 1664 = 344448

Step 1: Find the prime factorization of 1656

1656 = 2 x 2 x 2 x 3 x 3 x 23

Step 2: Find the prime factorization of 1664

1664 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 13

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

LCM = 344448 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 23

Step 4: Therefore, the least common multiple of 1656 and 1664 is 344448.