Least Common Multiple of 3968 and 3974

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3968 and 3974 the smallest integer that is 7884416 that is divisible by both numbers.

Least Common Multiple (LCM) of 3968 and 3974 is 7884416.

LCM(3968,3974) = 7884416

LCM of 3968 and 3974

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

LCM of:
and

Least Common Multiple of 3968 and 3974

LCM of 3968 and 3974 is 7884416

Least common multiple can be found by multiplying the highest exponent prime factors of 3968 and 3974. First we will calculate the prime factors of 3968 and 3974.

Prime Factorization of 3968


2 3968
2 1984
2 992
2 496
2 248
2 124
2 62
31 31
1

Prime factors of 3968 are 2,31. Prime factorization of 3968 in exponential form is:

3968 = 27×311

Prime Factorization of 3974


2 3974
1987 1987
1

Prime factors of 3974 are 2,1987. Prime factorization of 3974 in exponential form is:

3974 = 21×19871

Now multiplying the highest exponent prime factors to calculate the LCM of 3968 and 3974.

LCM(3968,3974) = 27×311×19871
LCM(3968,3974) = 7884416

Factors of 3968

List of positive integer factors of 3968 that divides 3968 without a remainder.

1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 128, 248, 496, 992, 1984, 3968

Factors of 3974

List of positive integer factors of 3974 that divides 3974 without a remainder.

1, 2, 1987, 3974

Least Common Multiple of 3968 and 3974 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3968 and 3974, than apply into the LCM equation.

GCF(3968,3974) = 2
LCM(3968,3974) = ( 3968 × 3974) / 2
LCM(3968,3974) = 15768832 / 2
LCM(3968,3974) = 7884416

Properties of LCM 3968 and 3974

(i) The LCM of 3974 and 3968 is associative

LCM of 3968 and 3974 = LCM of 3974 and 3968

Related Least Common Multiples of 3968

Related Least Common Multiples of 3974

Frequently Asked Questions on LCM of 3968 and 3974

1. What is the LCM of 3968 and 3974?

Answer: LCM of 3968 and 3974 is 7884416.

2. What are the Factors of 3968?

Answer: Factors of 3968 are 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 128, 248, 496, 992, 1984, 3968. There are 16 integers that are factors of 3968. The greatest factor of 3968 is 3968.

3. What are the Factors of 3974?

Answer: Factors of 3974 are 1, 2, 1987, 3974. There are 4 integers that are factors of 3974. The greatest factor of 3974 is 3974.

4. How to Find the LCM of 3968 and 3974?

Answer:

Least Common Multiple of 3968 and 3974 = 7884416

Step 1: Find the prime factorization of 3968

3968 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 31

Step 2: Find the prime factorization of 3974

3974 = 2 x 1987

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

LCM = 7884416 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 31 x 1987

Step 4: Therefore, the least common multiple of 3968 and 3974 is 7884416.