Least Common Multiple of 1224 and 1232

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1224 and 1232 the smallest integer that is 188496 that is divisible by both numbers.

Least Common Multiple (LCM) of 1224 and 1232 is 188496.

LCM(1224,1232) = 188496

LCM of 1224 and 1232

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

LCM of:
and

Least Common Multiple of 1224 and 1232

LCM of 1224 and 1232 is 188496

Least common multiple can be found by multiplying the highest exponent prime factors of 1224 and 1232. First we will calculate the prime factors of 1224 and 1232.

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

Prime Factorization of 1232


2 1232
2 616
2 308
2 154
7 77
11 11
1

Prime factors of 1232 are 2, 7,11. Prime factorization of 1232 in exponential form is:

1232 = 24×71×111

Now multiplying the highest exponent prime factors to calculate the LCM of 1224 and 1232.

LCM(1224,1232) = 24×32×71×111×171
LCM(1224,1232) = 188496

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

Factors of 1232

List of positive integer factors of 1232 that divides 1232 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 44, 56, 77, 88, 112, 154, 176, 308, 616, 1232

Least Common Multiple of 1224 and 1232 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1224 and 1232, than apply into the LCM equation.

GCF(1224,1232) = 8
LCM(1224,1232) = ( 1224 × 1232) / 8
LCM(1224,1232) = 1507968 / 8
LCM(1224,1232) = 188496

Properties of LCM 1224 and 1232

(i) The LCM of 1232 and 1224 is associative

LCM of 1224 and 1232 = LCM of 1232 and 1224

Related Least Common Multiples of 1224

Related Least Common Multiples of 1232

Frequently Asked Questions on LCM of 1224 and 1232

1. What is the LCM of 1224 and 1232?

Answer: LCM of 1224 and 1232 is 188496.

2. 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.

3. What are the Factors of 1232?

Answer: Factors of 1232 are 1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 44, 56, 77, 88, 112, 154, 176, 308, 616, 1232. There are 20 integers that are factors of 1232. The greatest factor of 1232 is 1232.

4. How to Find the LCM of 1224 and 1232?

Answer:

Least Common Multiple of 1224 and 1232 = 188496

Step 1: Find the prime factorization of 1224

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

Step 2: Find the prime factorization of 1232

1232 = 2 x 2 x 2 x 2 x 7 x 11

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

LCM = 188496 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 11 x 17

Step 4: Therefore, the least common multiple of 1224 and 1232 is 188496.