Least Common Multiple of 1960 and 1968

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1960 and 1968 the smallest integer that is 482160 that is divisible by both numbers.

Least Common Multiple (LCM) of 1960 and 1968 is 482160.

LCM(1960,1968) = 482160

LCM of 1960 and 1968

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

LCM of:
and

Least Common Multiple of 1960 and 1968

LCM of 1960 and 1968 is 482160

Least common multiple can be found by multiplying the highest exponent prime factors of 1960 and 1968. First we will calculate the prime factors of 1960 and 1968.

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

Prime Factorization of 1968


2 1968
2 984
2 492
2 246
3 123
41 41
1

Prime factors of 1968 are 2, 3,41. Prime factorization of 1968 in exponential form is:

1968 = 24×31×411

Now multiplying the highest exponent prime factors to calculate the LCM of 1960 and 1968.

LCM(1960,1968) = 24×31×51×72×411
LCM(1960,1968) = 482160

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

Factors of 1968

List of positive integer factors of 1968 that divides 1968 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 41, 48, 82, 123, 164, 246, 328, 492, 656, 984, 1968

Least Common Multiple of 1960 and 1968 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1960 and 1968, than apply into the LCM equation.

GCF(1960,1968) = 8
LCM(1960,1968) = ( 1960 × 1968) / 8
LCM(1960,1968) = 3857280 / 8
LCM(1960,1968) = 482160

Properties of LCM 1960 and 1968

(i) The LCM of 1968 and 1960 is associative

LCM of 1960 and 1968 = LCM of 1968 and 1960

Related Least Common Multiples of 1960

Related Least Common Multiples of 1968

Frequently Asked Questions on LCM of 1960 and 1968

1. What is the LCM of 1960 and 1968?

Answer: LCM of 1960 and 1968 is 482160.

2. 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.

3. What are the Factors of 1968?

Answer: Factors of 1968 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 41, 48, 82, 123, 164, 246, 328, 492, 656, 984, 1968. There are 20 integers that are factors of 1968. The greatest factor of 1968 is 1968.

4. How to Find the LCM of 1960 and 1968?

Answer:

Least Common Multiple of 1960 and 1968 = 482160

Step 1: Find the prime factorization of 1960

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

Step 2: Find the prime factorization of 1968

1968 = 2 x 2 x 2 x 2 x 3 x 41

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

LCM = 482160 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7 x 41

Step 4: Therefore, the least common multiple of 1960 and 1968 is 482160.