Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3500 and 3504 the smallest integer that is 3066000 that is divisible by both numbers.
Least Common Multiple (LCM) of 3500 and 3504 is 3066000.
LCM(3500,3504) = 3066000
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 3500 and 3504. First we will calculate the prime factors of 3500 and 3504.
Prime Factorization of 3500
2 | 3500 |
2 | 1750 |
5 | 875 |
5 | 175 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 3500 are 2, 5,7. Prime factorization of 3500 in exponential form is:
3500 = 22×53×71
Prime Factorization of 3504
2 | 3504 |
2 | 1752 |
2 | 876 |
2 | 438 |
3 | 219 |
73 | 73 |
1 |
Prime factors of 3504 are 2, 3,73. Prime factorization of 3504 in exponential form is:
3504 = 24×31×731
Now multiplying the highest exponent prime factors to calculate the LCM of 3500 and 3504.
LCM(3500,3504) = 24×31×53×71×731
LCM(3500,3504) = 3066000
Factors of 3500
List of positive integer factors of 3500 that divides 3500 without a remainder.
1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500
Factors of 3504
List of positive integer factors of 3504 that divides 3504 without a remainder.
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 73, 146, 219, 292, 438, 584, 876, 1168, 1752, 3504
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3500 and 3504, than apply into the LCM equation.
GCF(3500,3504) = 4
LCM(3500,3504) = ( 3500 × 3504) / 4
LCM(3500,3504) = 12264000 / 4
LCM(3500,3504) = 3066000
(i) The LCM of 3504 and 3500 is associative
LCM of 3500 and 3504 = LCM of 3504 and 3500
1. What is the LCM of 3500 and 3504?
Answer: LCM of 3500 and 3504 is 3066000.
2. What are the Factors of 3500?
Answer: Factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500. There are 24 integers that are factors of 3500. The greatest factor of 3500 is 3500.
3. What are the Factors of 3504?
Answer: Factors of 3504 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 73, 146, 219, 292, 438, 584, 876, 1168, 1752, 3504. There are 20 integers that are factors of 3504. The greatest factor of 3504 is 3504.
4. How to Find the LCM of 3500 and 3504?
Answer:
Least Common Multiple of 3500 and 3504 = 3066000
Step 1: Find the prime factorization of 3500
3500 = 2 x 2 x 5 x 5 x 5 x 7
Step 2: Find the prime factorization of 3504
3504 = 2 x 2 x 2 x 2 x 3 x 73
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3066000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 7 x 73
Step 4: Therefore, the least common multiple of 3500 and 3504 is 3066000.