Least Common Multiple of 2250 and 2256

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2250 and 2256 the smallest integer that is 846000 that is divisible by both numbers.

Least Common Multiple (LCM) of 2250 and 2256 is 846000.

LCM(2250,2256) = 846000

LCM of 2250 and 2256

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

LCM of:
and

Least Common Multiple of 2250 and 2256

LCM of 2250 and 2256 is 846000

Least common multiple can be found by multiplying the highest exponent prime factors of 2250 and 2256. First we will calculate the prime factors of 2250 and 2256.

Prime Factorization of 2250


2 2250
3 1125
3 375
5 125
5 25
5 5
1

Prime factors of 2250 are 2, 3,5. Prime factorization of 2250 in exponential form is:

2250 = 21×32×53

Prime Factorization of 2256


2 2256
2 1128
2 564
2 282
3 141
47 47
1

Prime factors of 2256 are 2, 3,47. Prime factorization of 2256 in exponential form is:

2256 = 24×31×471

Now multiplying the highest exponent prime factors to calculate the LCM of 2250 and 2256.

LCM(2250,2256) = 24×32×53×471
LCM(2250,2256) = 846000

Factors of 2250

List of positive integer factors of 2250 that divides 2250 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 125, 150, 225, 250, 375, 450, 750, 1125, 2250

Factors of 2256

List of positive integer factors of 2256 that divides 2256 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 47, 48, 94, 141, 188, 282, 376, 564, 752, 1128, 2256

Least Common Multiple of 2250 and 2256 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2250 and 2256, than apply into the LCM equation.

GCF(2250,2256) = 6
LCM(2250,2256) = ( 2250 × 2256) / 6
LCM(2250,2256) = 5076000 / 6
LCM(2250,2256) = 846000

Properties of LCM 2250 and 2256

(i) The LCM of 2256 and 2250 is associative

LCM of 2250 and 2256 = LCM of 2256 and 2250

Related Least Common Multiples of 2250

Related Least Common Multiples of 2256

Frequently Asked Questions on LCM of 2250 and 2256

1. What is the LCM of 2250 and 2256?

Answer: LCM of 2250 and 2256 is 846000.

2. What are the Factors of 2250?

Answer: Factors of 2250 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 125, 150, 225, 250, 375, 450, 750, 1125, 2250. There are 24 integers that are factors of 2250. The greatest factor of 2250 is 2250.

3. What are the Factors of 2256?

Answer: Factors of 2256 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 47, 48, 94, 141, 188, 282, 376, 564, 752, 1128, 2256. There are 20 integers that are factors of 2256. The greatest factor of 2256 is 2256.

4. How to Find the LCM of 2250 and 2256?

Answer:

Least Common Multiple of 2250 and 2256 = 846000

Step 1: Find the prime factorization of 2250

2250 = 2 x 3 x 3 x 5 x 5 x 5

Step 2: Find the prime factorization of 2256

2256 = 2 x 2 x 2 x 2 x 3 x 47

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

LCM = 846000 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 47

Step 4: Therefore, the least common multiple of 2250 and 2256 is 846000.