Least Common Multiple of 1968 and 1974

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 1974 the smallest integer that is 647472 that is divisible by both numbers.

Least Common Multiple (LCM) of 1968 and 1974 is 647472.

LCM(1968,1974) = 647472

LCM of 1968 and 1974

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

LCM of:
and

Least Common Multiple of 1968 and 1974

LCM of 1968 and 1974 is 647472

Least common multiple can be found by multiplying the highest exponent prime factors of 1968 and 1974. First we will calculate the prime factors of 1968 and 1974.

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 1974


2 1974
3 987
7 329
47 47
1

Prime factors of 1974 are 2, 3, 7,47. Prime factorization of 1974 in exponential form is:

1974 = 21×31×71×471

Now multiplying the highest exponent prime factors to calculate the LCM of 1968 and 1974.

LCM(1968,1974) = 24×31×71×411×471
LCM(1968,1974) = 647472

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 1974

List of positive integer factors of 1974 that divides 1974 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 47, 94, 141, 282, 329, 658, 987, 1974

Least Common Multiple of 1968 and 1974 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 1974, than apply into the LCM equation.

GCF(1968,1974) = 6
LCM(1968,1974) = ( 1968 × 1974) / 6
LCM(1968,1974) = 3884832 / 6
LCM(1968,1974) = 647472

Properties of LCM 1968 and 1974

(i) The LCM of 1974 and 1968 is associative

LCM of 1968 and 1974 = LCM of 1974 and 1968

Related Least Common Multiples of 1968

Related Least Common Multiples of 1974

Frequently Asked Questions on LCM of 1968 and 1974

1. What is the LCM of 1968 and 1974?

Answer: LCM of 1968 and 1974 is 647472.

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 1974?

Answer: Factors of 1974 are 1, 2, 3, 6, 7, 14, 21, 42, 47, 94, 141, 282, 329, 658, 987, 1974. There are 16 integers that are factors of 1974. The greatest factor of 1974 is 1974.

4. How to Find the LCM of 1968 and 1974?

Answer:

Least Common Multiple of 1968 and 1974 = 647472

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 1974

1974 = 2 x 3 x 7 x 47

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

LCM = 647472 = 2 x 2 x 2 x 2 x 3 x 7 x 41 x 47

Step 4: Therefore, the least common multiple of 1968 and 1974 is 647472.