Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2252 and 2256 the smallest integer that is 1270128 that is divisible by both numbers.
Least Common Multiple (LCM) of 2252 and 2256 is 1270128.
LCM(2252,2256) = 1270128
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 2252 and 2256. First we will calculate the prime factors of 2252 and 2256.
Prime Factorization of 2252
2 | 2252 |
2 | 1126 |
563 | 563 |
1 |
Prime factors of 2252 are 2,563. Prime factorization of 2252 in exponential form is:
2252 = 22×5631
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 2252 and 2256.
LCM(2252,2256) = 24×31×471×5631
LCM(2252,2256) = 1270128
Factors of 2252
List of positive integer factors of 2252 that divides 2252 without a remainder.
1, 2, 4, 563, 1126, 2252
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
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2252 and 2256, than apply into the LCM equation.
GCF(2252,2256) = 4
LCM(2252,2256) = ( 2252 × 2256) / 4
LCM(2252,2256) = 5080512 / 4
LCM(2252,2256) = 1270128
(i) The LCM of 2256 and 2252 is associative
LCM of 2252 and 2256 = LCM of 2256 and 2252
1. What is the LCM of 2252 and 2256?
Answer: LCM of 2252 and 2256 is 1270128.
2. What are the Factors of 2252?
Answer: Factors of 2252 are 1, 2, 4, 563, 1126, 2252. There are 6 integers that are factors of 2252. The greatest factor of 2252 is 2252.
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 2252 and 2256?
Answer:
Least Common Multiple of 2252 and 2256 = 1270128
Step 1: Find the prime factorization of 2252
2252 = 2 x 2 x 563
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 = 1270128 = 2 x 2 x 2 x 2 x 3 x 47 x 563
Step 4: Therefore, the least common multiple of 2252 and 2256 is 1270128.