Least Common Multiple of 1952 and 1960

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1952 and 1960 the smallest integer that is 478240 that is divisible by both numbers.

Least Common Multiple (LCM) of 1952 and 1960 is 478240.

LCM(1952,1960) = 478240

LCM of 1952 and 1960

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

LCM of:
and

Least Common Multiple of 1952 and 1960

LCM of 1952 and 1960 is 478240

Least common multiple can be found by multiplying the highest exponent prime factors of 1952 and 1960. First we will calculate the prime factors of 1952 and 1960.

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

Prime Factorization of 1960


2 1960
2 980
2 490
5 245
7 49
7 7
1

Prime factors of 1960 are 2, 5,7. Prime factorization of 1960 in exponential form is:

1960 = 23×51×72

Now multiplying the highest exponent prime factors to calculate the LCM of 1952 and 1960.

LCM(1952,1960) = 25×51×72×611
LCM(1952,1960) = 478240

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

Factors of 1960

List of positive integer factors of 1960 that divides 1960 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 49, 56, 70, 98, 140, 196, 245, 280, 392, 490, 980, 1960

Least Common Multiple of 1952 and 1960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1952 and 1960, than apply into the LCM equation.

GCF(1952,1960) = 8
LCM(1952,1960) = ( 1952 × 1960) / 8
LCM(1952,1960) = 3825920 / 8
LCM(1952,1960) = 478240

Properties of LCM 1952 and 1960

(i) The LCM of 1960 and 1952 is associative

LCM of 1952 and 1960 = LCM of 1960 and 1952

Related Least Common Multiples of 1952

Related Least Common Multiples of 1960

Frequently Asked Questions on LCM of 1952 and 1960

1. What is the LCM of 1952 and 1960?

Answer: LCM of 1952 and 1960 is 478240.

2. 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.

3. What are the Factors of 1960?

Answer: Factors of 1960 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 49, 56, 70, 98, 140, 196, 245, 280, 392, 490, 980, 1960. There are 24 integers that are factors of 1960. The greatest factor of 1960 is 1960.

4. How to Find the LCM of 1952 and 1960?

Answer:

Least Common Multiple of 1952 and 1960 = 478240

Step 1: Find the prime factorization of 1952

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

Step 2: Find the prime factorization of 1960

1960 = 2 x 2 x 2 x 5 x 7 x 7

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

LCM = 478240 = 2 x 2 x 2 x 2 x 2 x 5 x 7 x 7 x 61

Step 4: Therefore, the least common multiple of 1952 and 1960 is 478240.