Least Common Multiple of 1978 and 1984

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1978 and 1984 the smallest integer that is 1962176 that is divisible by both numbers.

Least Common Multiple (LCM) of 1978 and 1984 is 1962176.

LCM(1978,1984) = 1962176

LCM of 1978 and 1984

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

LCM of:
and

Least Common Multiple of 1978 and 1984

LCM of 1978 and 1984 is 1962176

Least common multiple can be found by multiplying the highest exponent prime factors of 1978 and 1984. First we will calculate the prime factors of 1978 and 1984.

Prime Factorization of 1978


2 1978
23 989
43 43
1

Prime factors of 1978 are 2, 23,43. Prime factorization of 1978 in exponential form is:

1978 = 21×231×431

Prime Factorization of 1984


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

Prime factors of 1984 are 2,31. Prime factorization of 1984 in exponential form is:

1984 = 26×311

Now multiplying the highest exponent prime factors to calculate the LCM of 1978 and 1984.

LCM(1978,1984) = 26×231×311×431
LCM(1978,1984) = 1962176

Factors of 1978

List of positive integer factors of 1978 that divides 1978 without a remainder.

1, 2, 23, 43, 46, 86, 989, 1978

Factors of 1984

List of positive integer factors of 1984 that divides 1984 without a remainder.

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

Least Common Multiple of 1978 and 1984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1978 and 1984, than apply into the LCM equation.

GCF(1978,1984) = 2
LCM(1978,1984) = ( 1978 × 1984) / 2
LCM(1978,1984) = 3924352 / 2
LCM(1978,1984) = 1962176

Properties of LCM 1978 and 1984

(i) The LCM of 1984 and 1978 is associative

LCM of 1978 and 1984 = LCM of 1984 and 1978

Related Least Common Multiples of 1978

Related Least Common Multiples of 1984

Frequently Asked Questions on LCM of 1978 and 1984

1. What is the LCM of 1978 and 1984?

Answer: LCM of 1978 and 1984 is 1962176.

2. What are the Factors of 1978?

Answer: Factors of 1978 are 1, 2, 23, 43, 46, 86, 989, 1978. There are 8 integers that are factors of 1978. The greatest factor of 1978 is 1978.

3. What are the Factors of 1984?

Answer: Factors of 1984 are 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992, 1984. There are 14 integers that are factors of 1984. The greatest factor of 1984 is 1984.

4. How to Find the LCM of 1978 and 1984?

Answer:

Least Common Multiple of 1978 and 1984 = 1962176

Step 1: Find the prime factorization of 1978

1978 = 2 x 23 x 43

Step 2: Find the prime factorization of 1984

1984 = 2 x 2 x 2 x 2 x 2 x 2 x 31

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

LCM = 1962176 = 2 x 2 x 2 x 2 x 2 x 2 x 23 x 31 x 43

Step 4: Therefore, the least common multiple of 1978 and 1984 is 1962176.