Least Common Multiple of 1968 and 1972

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1968 and 1972 the smallest integer that is 970224 that is divisible by both numbers.

Least Common Multiple (LCM) of 1968 and 1972 is 970224.

LCM(1968,1972) = 970224

LCM of 1968 and 1972

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

LCM of:
and

Least Common Multiple of 1968 and 1972

LCM of 1968 and 1972 is 970224

Least common multiple can be found by multiplying the highest exponent prime factors of 1968 and 1972. First we will calculate the prime factors of 1968 and 1972.

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

Prime Factorization of 1972


2 1972
2 986
17 493
29 29
1

Prime factors of 1972 are 2, 17,29. Prime factorization of 1972 in exponential form is:

1972 = 22×171×291

Now multiplying the highest exponent prime factors to calculate the LCM of 1968 and 1972.

LCM(1968,1972) = 24×31×171×291×411
LCM(1968,1972) = 970224

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

Factors of 1972

List of positive integer factors of 1972 that divides 1972 without a remainder.

1, 2, 4, 17, 29, 34, 58, 68, 116, 493, 986, 1972

Least Common Multiple of 1968 and 1972 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1968 and 1972, than apply into the LCM equation.

GCF(1968,1972) = 4
LCM(1968,1972) = ( 1968 × 1972) / 4
LCM(1968,1972) = 3880896 / 4
LCM(1968,1972) = 970224

Properties of LCM 1968 and 1972

(i) The LCM of 1972 and 1968 is associative

LCM of 1968 and 1972 = LCM of 1972 and 1968

Related Least Common Multiples of 1968

Related Least Common Multiples of 1972

Frequently Asked Questions on LCM of 1968 and 1972

1. What is the LCM of 1968 and 1972?

Answer: LCM of 1968 and 1972 is 970224.

2. 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.

3. What are the Factors of 1972?

Answer: Factors of 1972 are 1, 2, 4, 17, 29, 34, 58, 68, 116, 493, 986, 1972. There are 12 integers that are factors of 1972. The greatest factor of 1972 is 1972.

4. How to Find the LCM of 1968 and 1972?

Answer:

Least Common Multiple of 1968 and 1972 = 970224

Step 1: Find the prime factorization of 1968

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

Step 2: Find the prime factorization of 1972

1972 = 2 x 2 x 17 x 29

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

LCM = 970224 = 2 x 2 x 2 x 2 x 3 x 17 x 29 x 41

Step 4: Therefore, the least common multiple of 1968 and 1972 is 970224.