Least Common Multiple of 1209 and 1214

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1209 and 1214 the smallest integer that is 1467726 that is divisible by both numbers.

Least Common Multiple (LCM) of 1209 and 1214 is 1467726.

LCM(1209,1214) = 1467726

LCM of 1209 and 1214

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

LCM of:
and

Least Common Multiple of 1209 and 1214

LCM of 1209 and 1214 is 1467726

Least common multiple can be found by multiplying the highest exponent prime factors of 1209 and 1214. First we will calculate the prime factors of 1209 and 1214.

Prime Factorization of 1209


3 1209
13 403
31 31
1

Prime factors of 1209 are 3, 13,31. Prime factorization of 1209 in exponential form is:

1209 = 31×131×311

Prime Factorization of 1214


2 1214
607 607
1

Prime factors of 1214 are 2,607. Prime factorization of 1214 in exponential form is:

1214 = 21×6071

Now multiplying the highest exponent prime factors to calculate the LCM of 1209 and 1214.

LCM(1209,1214) = 21×31×131×311×6071
LCM(1209,1214) = 1467726

Factors of 1209

List of positive integer factors of 1209 that divides 1209 without a remainder.

1, 3, 13, 31, 39, 93, 403, 1209

Factors of 1214

List of positive integer factors of 1214 that divides 1214 without a remainder.

1, 2, 607, 1214

Least Common Multiple of 1209 and 1214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1209 and 1214, than apply into the LCM equation.

GCF(1209,1214) = 1
LCM(1209,1214) = ( 1209 × 1214) / 1
LCM(1209,1214) = 1467726 / 1
LCM(1209,1214) = 1467726

Properties of LCM 1209 and 1214

(i) The LCM of 1214 and 1209 is associative

LCM of 1209 and 1214 = LCM of 1214 and 1209

Related Least Common Multiples of 1209

Related Least Common Multiples of 1214

Frequently Asked Questions on LCM of 1209 and 1214

1. What is the LCM of 1209 and 1214?

Answer: LCM of 1209 and 1214 is 1467726.

2. What are the Factors of 1209?

Answer: Factors of 1209 are 1, 3, 13, 31, 39, 93, 403, 1209. There are 8 integers that are factors of 1209. The greatest factor of 1209 is 1209.

3. What are the Factors of 1214?

Answer: Factors of 1214 are 1, 2, 607, 1214. There are 4 integers that are factors of 1214. The greatest factor of 1214 is 1214.

4. How to Find the LCM of 1209 and 1214?

Answer:

Least Common Multiple of 1209 and 1214 = 1467726

Step 1: Find the prime factorization of 1209

1209 = 3 x 13 x 31

Step 2: Find the prime factorization of 1214

1214 = 2 x 607

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

LCM = 1467726 = 2 x 3 x 13 x 31 x 607

Step 4: Therefore, the least common multiple of 1209 and 1214 is 1467726.