Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1528 and 1536 the smallest integer that is 293376 that is divisible by both numbers.
Least Common Multiple (LCM) of 1528 and 1536 is 293376.
LCM(1528,1536) = 293376
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 1528 and 1536. First we will calculate the prime factors of 1528 and 1536.
Prime Factorization of 1528
2 | 1528 |
2 | 764 |
2 | 382 |
191 | 191 |
1 |
Prime factors of 1528 are 2,191. Prime factorization of 1528 in exponential form is:
1528 = 23×1911
Prime Factorization of 1536
2 | 1536 |
2 | 768 |
2 | 384 |
2 | 192 |
2 | 96 |
2 | 48 |
2 | 24 |
2 | 12 |
2 | 6 |
3 | 3 |
1 |
Prime factors of 1536 are 2,3. Prime factorization of 1536 in exponential form is:
1536 = 29×31
Now multiplying the highest exponent prime factors to calculate the LCM of 1528 and 1536.
LCM(1528,1536) = 29×31×1911
LCM(1528,1536) = 293376
Factors of 1528
List of positive integer factors of 1528 that divides 1528 without a remainder.
1, 2, 4, 8, 191, 382, 764, 1528
Factors of 1536
List of positive integer factors of 1536 that divides 1536 without a remainder.
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1528 and 1536, than apply into the LCM equation.
GCF(1528,1536) = 8
LCM(1528,1536) = ( 1528 × 1536) / 8
LCM(1528,1536) = 2347008 / 8
LCM(1528,1536) = 293376
(i) The LCM of 1536 and 1528 is associative
LCM of 1528 and 1536 = LCM of 1536 and 1528
1. What is the LCM of 1528 and 1536?
Answer: LCM of 1528 and 1536 is 293376.
2. What are the Factors of 1528?
Answer: Factors of 1528 are 1, 2, 4, 8, 191, 382, 764, 1528. There are 8 integers that are factors of 1528. The greatest factor of 1528 is 1528.
3. What are the Factors of 1536?
Answer: Factors of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536. There are 20 integers that are factors of 1536. The greatest factor of 1536 is 1536.
4. How to Find the LCM of 1528 and 1536?
Answer:
Least Common Multiple of 1528 and 1536 = 293376
Step 1: Find the prime factorization of 1528
1528 = 2 x 2 x 2 x 191
Step 2: Find the prime factorization of 1536
1536 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 293376 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 191
Step 4: Therefore, the least common multiple of 1528 and 1536 is 293376.