Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1577 and 1584 the smallest integer that is 2497968 that is divisible by both numbers.
Least Common Multiple (LCM) of 1577 and 1584 is 2497968.
LCM(1577,1584) = 2497968
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 1577 and 1584. First we will calculate the prime factors of 1577 and 1584.
Prime Factorization of 1577
19 | 1577 |
83 | 83 |
1 |
Prime factors of 1577 are 19,83. Prime factorization of 1577 in exponential form is:
1577 = 191×831
Prime Factorization of 1584
2 | 1584 |
2 | 792 |
2 | 396 |
2 | 198 |
3 | 99 |
3 | 33 |
11 | 11 |
1 |
Prime factors of 1584 are 2, 3,11. Prime factorization of 1584 in exponential form is:
1584 = 24×32×111
Now multiplying the highest exponent prime factors to calculate the LCM of 1577 and 1584.
LCM(1577,1584) = 24×32×111×191×831
LCM(1577,1584) = 2497968
Factors of 1577
List of positive integer factors of 1577 that divides 1577 without a remainder.
1, 19, 83, 1577
Factors of 1584
List of positive integer factors of 1584 that divides 1584 without a remainder.
1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 66, 72, 88, 99, 132, 144, 176, 198, 264, 396, 528, 792, 1584
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1577 and 1584, than apply into the LCM equation.
GCF(1577,1584) = 1
LCM(1577,1584) = ( 1577 × 1584) / 1
LCM(1577,1584) = 2497968 / 1
LCM(1577,1584) = 2497968
(i) The LCM of 1584 and 1577 is associative
LCM of 1577 and 1584 = LCM of 1584 and 1577
1. What is the LCM of 1577 and 1584?
Answer: LCM of 1577 and 1584 is 2497968.
2. What are the Factors of 1577?
Answer: Factors of 1577 are 1, 19, 83, 1577. There are 4 integers that are factors of 1577. The greatest factor of 1577 is 1577.
3. What are the Factors of 1584?
Answer: Factors of 1584 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 66, 72, 88, 99, 132, 144, 176, 198, 264, 396, 528, 792, 1584. There are 30 integers that are factors of 1584. The greatest factor of 1584 is 1584.
4. How to Find the LCM of 1577 and 1584?
Answer:
Least Common Multiple of 1577 and 1584 = 2497968
Step 1: Find the prime factorization of 1577
1577 = 19 x 83
Step 2: Find the prime factorization of 1584
1584 = 2 x 2 x 2 x 2 x 3 x 3 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2497968 = 2 x 2 x 2 x 2 x 3 x 3 x 11 x 19 x 83
Step 4: Therefore, the least common multiple of 1577 and 1584 is 2497968.