Least Common Multiple of 1200 and 1206

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1200 and 1206 the smallest integer that is 241200 that is divisible by both numbers.

Least Common Multiple (LCM) of 1200 and 1206 is 241200.

LCM(1200,1206) = 241200

LCM of 1200 and 1206

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

LCM of:
and

Least Common Multiple of 1200 and 1206

LCM of 1200 and 1206 is 241200

Least common multiple can be found by multiplying the highest exponent prime factors of 1200 and 1206. First we will calculate the prime factors of 1200 and 1206.

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

Prime Factorization of 1206


2 1206
3 603
3 201
67 67
1

Prime factors of 1206 are 2, 3,67. Prime factorization of 1206 in exponential form is:

1206 = 21×32×671

Now multiplying the highest exponent prime factors to calculate the LCM of 1200 and 1206.

LCM(1200,1206) = 24×32×52×671
LCM(1200,1206) = 241200

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

Factors of 1206

List of positive integer factors of 1206 that divides 1206 without a remainder.

1, 2, 3, 6, 9, 18, 67, 134, 201, 402, 603, 1206

Least Common Multiple of 1200 and 1206 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1200 and 1206, than apply into the LCM equation.

GCF(1200,1206) = 6
LCM(1200,1206) = ( 1200 × 1206) / 6
LCM(1200,1206) = 1447200 / 6
LCM(1200,1206) = 241200

Properties of LCM 1200 and 1206

(i) The LCM of 1206 and 1200 is associative

LCM of 1200 and 1206 = LCM of 1206 and 1200

Related Least Common Multiples of 1200

Related Least Common Multiples of 1206

Frequently Asked Questions on LCM of 1200 and 1206

1. What is the LCM of 1200 and 1206?

Answer: LCM of 1200 and 1206 is 241200.

2. 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.

3. What are the Factors of 1206?

Answer: Factors of 1206 are 1, 2, 3, 6, 9, 18, 67, 134, 201, 402, 603, 1206. There are 12 integers that are factors of 1206. The greatest factor of 1206 is 1206.

4. How to Find the LCM of 1200 and 1206?

Answer:

Least Common Multiple of 1200 and 1206 = 241200

Step 1: Find the prime factorization of 1200

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

Step 2: Find the prime factorization of 1206

1206 = 2 x 3 x 3 x 67

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

LCM = 241200 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 67

Step 4: Therefore, the least common multiple of 1200 and 1206 is 241200.