Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1503 and 1506 the smallest integer that is 754506 that is divisible by both numbers.
Least Common Multiple (LCM) of 1503 and 1506 is 754506.
LCM(1503,1506) = 754506
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 1503 and 1506. First we will calculate the prime factors of 1503 and 1506.
Prime Factorization of 1503
3 | 1503 |
3 | 501 |
167 | 167 |
1 |
Prime factors of 1503 are 3,167. Prime factorization of 1503 in exponential form is:
1503 = 32×1671
Prime Factorization of 1506
2 | 1506 |
3 | 753 |
251 | 251 |
1 |
Prime factors of 1506 are 2, 3,251. Prime factorization of 1506 in exponential form is:
1506 = 21×31×2511
Now multiplying the highest exponent prime factors to calculate the LCM of 1503 and 1506.
LCM(1503,1506) = 21×32×1671×2511
LCM(1503,1506) = 754506
Factors of 1503
List of positive integer factors of 1503 that divides 1503 without a remainder.
1, 3, 9, 167, 501, 1503
Factors of 1506
List of positive integer factors of 1506 that divides 1506 without a remainder.
1, 2, 3, 6, 251, 502, 753, 1506
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1503 and 1506, than apply into the LCM equation.
GCF(1503,1506) = 3
LCM(1503,1506) = ( 1503 × 1506) / 3
LCM(1503,1506) = 2263518 / 3
LCM(1503,1506) = 754506
(i) The LCM of 1506 and 1503 is associative
LCM of 1503 and 1506 = LCM of 1506 and 1503
1. What is the LCM of 1503 and 1506?
Answer: LCM of 1503 and 1506 is 754506.
2. What are the Factors of 1503?
Answer: Factors of 1503 are 1, 3, 9, 167, 501, 1503. There are 6 integers that are factors of 1503. The greatest factor of 1503 is 1503.
3. What are the Factors of 1506?
Answer: Factors of 1506 are 1, 2, 3, 6, 251, 502, 753, 1506. There are 8 integers that are factors of 1506. The greatest factor of 1506 is 1506.
4. How to Find the LCM of 1503 and 1506?
Answer:
Least Common Multiple of 1503 and 1506 = 754506
Step 1: Find the prime factorization of 1503
1503 = 3 x 3 x 167
Step 2: Find the prime factorization of 1506
1506 = 2 x 3 x 251
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 754506 = 2 x 3 x 3 x 167 x 251
Step 4: Therefore, the least common multiple of 1503 and 1506 is 754506.