Least Common Multiple of 3978 and 3984

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3978 and 3984 the smallest integer that is 2641392 that is divisible by both numbers.

Least Common Multiple (LCM) of 3978 and 3984 is 2641392.

LCM(3978,3984) = 2641392

LCM of 3978 and 3984

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

LCM of:
and

Least Common Multiple of 3978 and 3984

LCM of 3978 and 3984 is 2641392

Least common multiple can be found by multiplying the highest exponent prime factors of 3978 and 3984. First we will calculate the prime factors of 3978 and 3984.

Prime Factorization of 3978


2 3978
3 1989
3 663
13 221
17 17
1

Prime factors of 3978 are 2, 3, 13,17. Prime factorization of 3978 in exponential form is:

3978 = 21×32×131×171

Prime Factorization of 3984


2 3984
2 1992
2 996
2 498
3 249
83 83
1

Prime factors of 3984 are 2, 3,83. Prime factorization of 3984 in exponential form is:

3984 = 24×31×831

Now multiplying the highest exponent prime factors to calculate the LCM of 3978 and 3984.

LCM(3978,3984) = 24×32×131×171×831
LCM(3978,3984) = 2641392

Factors of 3978

List of positive integer factors of 3978 that divides 3978 without a remainder.

1, 2, 3, 6, 9, 13, 17, 18, 26, 34, 39, 51, 78, 102, 117, 153, 221, 234, 306, 442, 663, 1326, 1989, 3978

Factors of 3984

List of positive integer factors of 3984 that divides 3984 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 83, 166, 249, 332, 498, 664, 996, 1328, 1992, 3984

Least Common Multiple of 3978 and 3984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3978 and 3984, than apply into the LCM equation.

GCF(3978,3984) = 6
LCM(3978,3984) = ( 3978 × 3984) / 6
LCM(3978,3984) = 15848352 / 6
LCM(3978,3984) = 2641392

Properties of LCM 3978 and 3984

(i) The LCM of 3984 and 3978 is associative

LCM of 3978 and 3984 = LCM of 3984 and 3978

Related Least Common Multiples of 3978

Related Least Common Multiples of 3984

Frequently Asked Questions on LCM of 3978 and 3984

1. What is the LCM of 3978 and 3984?

Answer: LCM of 3978 and 3984 is 2641392.

2. What are the Factors of 3978?

Answer: Factors of 3978 are 1, 2, 3, 6, 9, 13, 17, 18, 26, 34, 39, 51, 78, 102, 117, 153, 221, 234, 306, 442, 663, 1326, 1989, 3978. There are 24 integers that are factors of 3978. The greatest factor of 3978 is 3978.

3. What are the Factors of 3984?

Answer: Factors of 3984 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 83, 166, 249, 332, 498, 664, 996, 1328, 1992, 3984. There are 20 integers that are factors of 3984. The greatest factor of 3984 is 3984.

4. How to Find the LCM of 3978 and 3984?

Answer:

Least Common Multiple of 3978 and 3984 = 2641392

Step 1: Find the prime factorization of 3978

3978 = 2 x 3 x 3 x 13 x 17

Step 2: Find the prime factorization of 3984

3984 = 2 x 2 x 2 x 2 x 3 x 83

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

LCM = 2641392 = 2 x 2 x 2 x 2 x 3 x 3 x 13 x 17 x 83

Step 4: Therefore, the least common multiple of 3978 and 3984 is 2641392.