Least Common Multiple of 1920 and 1921

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1920 and 1921 the smallest integer that is 3688320 that is divisible by both numbers.

Least Common Multiple (LCM) of 1920 and 1921 is 3688320.

LCM(1920,1921) = 3688320

LCM of 1920 and 1921

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

LCM of:
and

Least Common Multiple of 1920 and 1921

LCM of 1920 and 1921 is 3688320

Least common multiple can be found by multiplying the highest exponent prime factors of 1920 and 1921. First we will calculate the prime factors of 1920 and 1921.

Prime Factorization of 1920


2 1920
2 960
2 480
2 240
2 120
2 60
2 30
3 15
5 5
1

Prime factors of 1920 are 2, 3,5. Prime factorization of 1920 in exponential form is:

1920 = 27×31×51

Prime Factorization of 1921


17 1921
113 113
1

Prime factors of 1921 are 17,113. Prime factorization of 1921 in exponential form is:

1921 = 171×1131

Now multiplying the highest exponent prime factors to calculate the LCM of 1920 and 1921.

LCM(1920,1921) = 27×31×51×171×1131
LCM(1920,1921) = 3688320

Factors of 1920

List of positive integer factors of 1920 that divides 1920 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1920

Factors of 1921

List of positive integer factors of 1921 that divides 1921 without a remainder.

1, 17, 113, 1921

Least Common Multiple of 1920 and 1921 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1920 and 1921, than apply into the LCM equation.

GCF(1920,1921) = 1
LCM(1920,1921) = ( 1920 × 1921) / 1
LCM(1920,1921) = 3688320 / 1
LCM(1920,1921) = 3688320

Properties of LCM 1920 and 1921

(i) The LCM of 1921 and 1920 is associative

LCM of 1920 and 1921 = LCM of 1921 and 1920

Related Least Common Multiples of 1920

Related Least Common Multiples of 1921

Frequently Asked Questions on LCM of 1920 and 1921

1. What is the LCM of 1920 and 1921?

Answer: LCM of 1920 and 1921 is 3688320.

2. What are the Factors of 1920?

Answer: Factors of 1920 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1920. There are 32 integers that are factors of 1920. The greatest factor of 1920 is 1920.

3. What are the Factors of 1921?

Answer: Factors of 1921 are 1, 17, 113, 1921. There are 4 integers that are factors of 1921. The greatest factor of 1921 is 1921.

4. How to Find the LCM of 1920 and 1921?

Answer:

Least Common Multiple of 1920 and 1921 = 3688320

Step 1: Find the prime factorization of 1920

1920 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 1921

1921 = 17 x 113

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

LCM = 3688320 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 17 x 113

Step 4: Therefore, the least common multiple of 1920 and 1921 is 3688320.