Least Common Multiple of 1953 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 1953 and 1960 the smallest integer that is 546840 that is divisible by both numbers.

Least Common Multiple (LCM) of 1953 and 1960 is 546840.

LCM(1953,1960) = 546840

LCM of 1953 and 1960

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

LCM of:
and

Least Common Multiple of 1953 and 1960

LCM of 1953 and 1960 is 546840

Least common multiple can be found by multiplying the highest exponent prime factors of 1953 and 1960. First we will calculate the prime factors of 1953 and 1960.

Prime Factorization of 1953


3 1953
3 651
7 217
31 31
1

Prime factors of 1953 are 3, 7,31. Prime factorization of 1953 in exponential form is:

1953 = 32×71×311

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 1953 and 1960.

LCM(1953,1960) = 23×32×51×72×311
LCM(1953,1960) = 546840

Factors of 1953

List of positive integer factors of 1953 that divides 1953 without a remainder.

1, 3, 7, 9, 21, 31, 63, 93, 217, 279, 651, 1953

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 1953 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 1953 and 1960, than apply into the LCM equation.

GCF(1953,1960) = 7
LCM(1953,1960) = ( 1953 × 1960) / 7
LCM(1953,1960) = 3827880 / 7
LCM(1953,1960) = 546840

Properties of LCM 1953 and 1960

(i) The LCM of 1960 and 1953 is associative

LCM of 1953 and 1960 = LCM of 1960 and 1953

Related Least Common Multiples of 1953

Related Least Common Multiples of 1960

Frequently Asked Questions on LCM of 1953 and 1960

1. What is the LCM of 1953 and 1960?

Answer: LCM of 1953 and 1960 is 546840.

2. What are the Factors of 1953?

Answer: Factors of 1953 are 1, 3, 7, 9, 21, 31, 63, 93, 217, 279, 651, 1953. There are 12 integers that are factors of 1953. The greatest factor of 1953 is 1953.

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 1953 and 1960?

Answer:

Least Common Multiple of 1953 and 1960 = 546840

Step 1: Find the prime factorization of 1953

1953 = 3 x 3 x 7 x 31

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 = 546840 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 7 x 31

Step 4: Therefore, the least common multiple of 1953 and 1960 is 546840.