Least Common Multiple of 1216 and 1224

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1216 and 1224 the smallest integer that is 186048 that is divisible by both numbers.

Least Common Multiple (LCM) of 1216 and 1224 is 186048.

LCM(1216,1224) = 186048

LCM of 1216 and 1224

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

LCM of:
and

Least Common Multiple of 1216 and 1224

LCM of 1216 and 1224 is 186048

Least common multiple can be found by multiplying the highest exponent prime factors of 1216 and 1224. First we will calculate the prime factors of 1216 and 1224.

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

Prime Factorization of 1224


2 1224
2 612
2 306
3 153
3 51
17 17
1

Prime factors of 1224 are 2, 3,17. Prime factorization of 1224 in exponential form is:

1224 = 23×32×171

Now multiplying the highest exponent prime factors to calculate the LCM of 1216 and 1224.

LCM(1216,1224) = 26×32×171×191
LCM(1216,1224) = 186048

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

Factors of 1224

List of positive integer factors of 1224 that divides 1224 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224

Least Common Multiple of 1216 and 1224 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1216 and 1224, than apply into the LCM equation.

GCF(1216,1224) = 8
LCM(1216,1224) = ( 1216 × 1224) / 8
LCM(1216,1224) = 1488384 / 8
LCM(1216,1224) = 186048

Properties of LCM 1216 and 1224

(i) The LCM of 1224 and 1216 is associative

LCM of 1216 and 1224 = LCM of 1224 and 1216

Related Least Common Multiples of 1216

Related Least Common Multiples of 1224

Frequently Asked Questions on LCM of 1216 and 1224

1. What is the LCM of 1216 and 1224?

Answer: LCM of 1216 and 1224 is 186048.

2. 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.

3. What are the Factors of 1224?

Answer: Factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224. There are 24 integers that are factors of 1224. The greatest factor of 1224 is 1224.

4. How to Find the LCM of 1216 and 1224?

Answer:

Least Common Multiple of 1216 and 1224 = 186048

Step 1: Find the prime factorization of 1216

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

Step 2: Find the prime factorization of 1224

1224 = 2 x 2 x 2 x 3 x 3 x 17

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

LCM = 186048 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 17 x 19

Step 4: Therefore, the least common multiple of 1216 and 1224 is 186048.