Least Common Multiple of 1209 and 1216

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 1216 the smallest integer that is 1470144 that is divisible by both numbers.

Least Common Multiple (LCM) of 1209 and 1216 is 1470144.

LCM(1209,1216) = 1470144

LCM of 1209 and 1216

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

LCM of:
and

Least Common Multiple of 1209 and 1216

LCM of 1209 and 1216 is 1470144

Least common multiple can be found by multiplying the highest exponent prime factors of 1209 and 1216. First we will calculate the prime factors of 1209 and 1216.

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 1216


2 1216
2 608
2 304
2 152
2 76
2 38
19 19
1

Prime factors of 1216 are 2,19. Prime factorization of 1216 in exponential form is:

1216 = 26×191

Now multiplying the highest exponent prime factors to calculate the LCM of 1209 and 1216.

LCM(1209,1216) = 26×31×131×191×311
LCM(1209,1216) = 1470144

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 1216

List of positive integer factors of 1216 that divides 1216 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 152, 304, 608, 1216

Least Common Multiple of 1209 and 1216 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 1216, than apply into the LCM equation.

GCF(1209,1216) = 1
LCM(1209,1216) = ( 1209 × 1216) / 1
LCM(1209,1216) = 1470144 / 1
LCM(1209,1216) = 1470144

Properties of LCM 1209 and 1216

(i) The LCM of 1216 and 1209 is associative

LCM of 1209 and 1216 = LCM of 1216 and 1209

Related Least Common Multiples of 1209

Related Least Common Multiples of 1216

Frequently Asked Questions on LCM of 1209 and 1216

1. What is the LCM of 1209 and 1216?

Answer: LCM of 1209 and 1216 is 1470144.

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 1216?

Answer: Factors of 1216 are 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 152, 304, 608, 1216. There are 14 integers that are factors of 1216. The greatest factor of 1216 is 1216.

4. How to Find the LCM of 1209 and 1216?

Answer:

Least Common Multiple of 1209 and 1216 = 1470144

Step 1: Find the prime factorization of 1209

1209 = 3 x 13 x 31

Step 2: Find the prime factorization of 1216

1216 = 2 x 2 x 2 x 2 x 2 x 2 x 19

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

LCM = 1470144 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 19 x 31

Step 4: Therefore, the least common multiple of 1209 and 1216 is 1470144.