Least Common Multiple of 1197 and 1200

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1197 and 1200 the smallest integer that is 478800 that is divisible by both numbers.

Least Common Multiple (LCM) of 1197 and 1200 is 478800.

LCM(1197,1200) = 478800

LCM of 1197 and 1200

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

LCM of:
and

Least Common Multiple of 1197 and 1200

LCM of 1197 and 1200 is 478800

Least common multiple can be found by multiplying the highest exponent prime factors of 1197 and 1200. First we will calculate the prime factors of 1197 and 1200.

Prime Factorization of 1197


3 1197
3 399
7 133
19 19
1

Prime factors of 1197 are 3, 7,19. Prime factorization of 1197 in exponential form is:

1197 = 32×71×191

Prime Factorization of 1200


2 1200
2 600
2 300
2 150
3 75
5 25
5 5
1

Prime factors of 1200 are 2, 3,5. Prime factorization of 1200 in exponential form is:

1200 = 24×31×52

Now multiplying the highest exponent prime factors to calculate the LCM of 1197 and 1200.

LCM(1197,1200) = 24×32×52×71×191
LCM(1197,1200) = 478800

Factors of 1197

List of positive integer factors of 1197 that divides 1197 without a remainder.

1, 3, 7, 9, 19, 21, 57, 63, 133, 171, 399, 1197

Factors of 1200

List of positive integer factors of 1200 that divides 1200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200

Least Common Multiple of 1197 and 1200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1197 and 1200, than apply into the LCM equation.

GCF(1197,1200) = 3
LCM(1197,1200) = ( 1197 × 1200) / 3
LCM(1197,1200) = 1436400 / 3
LCM(1197,1200) = 478800

Properties of LCM 1197 and 1200

(i) The LCM of 1200 and 1197 is associative

LCM of 1197 and 1200 = LCM of 1200 and 1197

Related Least Common Multiples of 1197

Related Least Common Multiples of 1200

Frequently Asked Questions on LCM of 1197 and 1200

1. What is the LCM of 1197 and 1200?

Answer: LCM of 1197 and 1200 is 478800.

2. What are the Factors of 1197?

Answer: Factors of 1197 are 1, 3, 7, 9, 19, 21, 57, 63, 133, 171, 399, 1197. There are 12 integers that are factors of 1197. The greatest factor of 1197 is 1197.

3. What are the Factors of 1200?

Answer: Factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200. There are 30 integers that are factors of 1200. The greatest factor of 1200 is 1200.

4. How to Find the LCM of 1197 and 1200?

Answer:

Least Common Multiple of 1197 and 1200 = 478800

Step 1: Find the prime factorization of 1197

1197 = 3 x 3 x 7 x 19

Step 2: Find the prime factorization of 1200

1200 = 2 x 2 x 2 x 2 x 3 x 5 x 5

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

LCM = 478800 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7 x 19

Step 4: Therefore, the least common multiple of 1197 and 1200 is 478800.