Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1521 and 1528 the smallest integer that is 2324088 that is divisible by both numbers.
Least Common Multiple (LCM) of 1521 and 1528 is 2324088.
LCM(1521,1528) = 2324088
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 1521 and 1528. First we will calculate the prime factors of 1521 and 1528.
Prime Factorization of 1521
3 | 1521 |
3 | 507 |
13 | 169 |
13 | 13 |
1 |
Prime factors of 1521 are 3,13. Prime factorization of 1521 in exponential form is:
1521 = 32×132
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
Now multiplying the highest exponent prime factors to calculate the LCM of 1521 and 1528.
LCM(1521,1528) = 23×32×132×1911
LCM(1521,1528) = 2324088
Factors of 1521
List of positive integer factors of 1521 that divides 1521 without a remainder.
1, 3, 9, 13, 39, 117, 169, 507, 1521
Factors of 1528
List of positive integer factors of 1528 that divides 1528 without a remainder.
1, 2, 4, 8, 191, 382, 764, 1528
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1521 and 1528, than apply into the LCM equation.
GCF(1521,1528) = 1
LCM(1521,1528) = ( 1521 × 1528) / 1
LCM(1521,1528) = 2324088 / 1
LCM(1521,1528) = 2324088
(i) The LCM of 1528 and 1521 is associative
LCM of 1521 and 1528 = LCM of 1528 and 1521
1. What is the LCM of 1521 and 1528?
Answer: LCM of 1521 and 1528 is 2324088.
2. What are the Factors of 1521?
Answer: Factors of 1521 are 1, 3, 9, 13, 39, 117, 169, 507, 1521. There are 9 integers that are factors of 1521. The greatest factor of 1521 is 1521.
3. 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.
4. How to Find the LCM of 1521 and 1528?
Answer:
Least Common Multiple of 1521 and 1528 = 2324088
Step 1: Find the prime factorization of 1521
1521 = 3 x 3 x 13 x 13
Step 2: Find the prime factorization of 1528
1528 = 2 x 2 x 2 x 191
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2324088 = 2 x 2 x 2 x 3 x 3 x 13 x 13 x 191
Step 4: Therefore, the least common multiple of 1521 and 1528 is 2324088.