Least Common Multiple of 1944 and 1952

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1944 and 1952 the smallest integer that is 474336 that is divisible by both numbers.

Least Common Multiple (LCM) of 1944 and 1952 is 474336.

LCM(1944,1952) = 474336

LCM of 1944 and 1952

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

LCM of:
and

Least Common Multiple of 1944 and 1952

LCM of 1944 and 1952 is 474336

Least common multiple can be found by multiplying the highest exponent prime factors of 1944 and 1952. First we will calculate the prime factors of 1944 and 1952.

Prime Factorization of 1944


2 1944
2 972
2 486
3 243
3 81
3 27
3 9
3 3
1

Prime factors of 1944 are 2,3. Prime factorization of 1944 in exponential form is:

1944 = 23×35

Prime Factorization of 1952


2 1952
2 976
2 488
2 244
2 122
61 61
1

Prime factors of 1952 are 2,61. Prime factorization of 1952 in exponential form is:

1952 = 25×611

Now multiplying the highest exponent prime factors to calculate the LCM of 1944 and 1952.

LCM(1944,1952) = 25×35×611
LCM(1944,1952) = 474336

Factors of 1944

List of positive integer factors of 1944 that divides 1944 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944

Factors of 1952

List of positive integer factors of 1952 that divides 1952 without a remainder.

1, 2, 4, 8, 16, 32, 61, 122, 244, 488, 976, 1952

Least Common Multiple of 1944 and 1952 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1944 and 1952, than apply into the LCM equation.

GCF(1944,1952) = 8
LCM(1944,1952) = ( 1944 × 1952) / 8
LCM(1944,1952) = 3794688 / 8
LCM(1944,1952) = 474336

Properties of LCM 1944 and 1952

(i) The LCM of 1952 and 1944 is associative

LCM of 1944 and 1952 = LCM of 1952 and 1944

Related Least Common Multiples of 1944

Related Least Common Multiples of 1952

Frequently Asked Questions on LCM of 1944 and 1952

1. What is the LCM of 1944 and 1952?

Answer: LCM of 1944 and 1952 is 474336.

2. What are the Factors of 1944?

Answer: Factors of 1944 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944. There are 24 integers that are factors of 1944. The greatest factor of 1944 is 1944.

3. What are the Factors of 1952?

Answer: Factors of 1952 are 1, 2, 4, 8, 16, 32, 61, 122, 244, 488, 976, 1952. There are 12 integers that are factors of 1952. The greatest factor of 1952 is 1952.

4. How to Find the LCM of 1944 and 1952?

Answer:

Least Common Multiple of 1944 and 1952 = 474336

Step 1: Find the prime factorization of 1944

1944 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3

Step 2: Find the prime factorization of 1952

1952 = 2 x 2 x 2 x 2 x 2 x 61

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

LCM = 474336 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 61

Step 4: Therefore, the least common multiple of 1944 and 1952 is 474336.