Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7875 and 7880 the smallest integer that is 12411000 that is divisible by both numbers.
Least Common Multiple (LCM) of 7875 and 7880 is 12411000.
LCM(7875,7880) = 12411000
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 7875 and 7880. First we will calculate the prime factors of 7875 and 7880.
Prime Factorization of 7875
3 | 7875 |
3 | 2625 |
5 | 875 |
5 | 175 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 7875 are 3, 5,7. Prime factorization of 7875 in exponential form is:
7875 = 32×53×71
Prime Factorization of 7880
2 | 7880 |
2 | 3940 |
2 | 1970 |
5 | 985 |
197 | 197 |
1 |
Prime factors of 7880 are 2, 5,197. Prime factorization of 7880 in exponential form is:
7880 = 23×51×1971
Now multiplying the highest exponent prime factors to calculate the LCM of 7875 and 7880.
LCM(7875,7880) = 23×32×53×71×1971
LCM(7875,7880) = 12411000
Factors of 7875
List of positive integer factors of 7875 that divides 7875 without a remainder.
1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 125, 175, 225, 315, 375, 525, 875, 1125, 1575, 2625, 7875
Factors of 7880
List of positive integer factors of 7880 that divides 7880 without a remainder.
1, 2, 4, 5, 8, 10, 20, 40, 197, 394, 788, 985, 1576, 1970, 3940, 7880
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7875 and 7880, than apply into the LCM equation.
GCF(7875,7880) = 5
LCM(7875,7880) = ( 7875 × 7880) / 5
LCM(7875,7880) = 62055000 / 5
LCM(7875,7880) = 12411000
(i) The LCM of 7880 and 7875 is associative
LCM of 7875 and 7880 = LCM of 7880 and 7875
1. What is the LCM of 7875 and 7880?
Answer: LCM of 7875 and 7880 is 12411000.
2. What are the Factors of 7875?
Answer: Factors of 7875 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 125, 175, 225, 315, 375, 525, 875, 1125, 1575, 2625, 7875. There are 24 integers that are factors of 7875. The greatest factor of 7875 is 7875.
3. What are the Factors of 7880?
Answer: Factors of 7880 are 1, 2, 4, 5, 8, 10, 20, 40, 197, 394, 788, 985, 1576, 1970, 3940, 7880. There are 16 integers that are factors of 7880. The greatest factor of 7880 is 7880.
4. How to Find the LCM of 7875 and 7880?
Answer:
Least Common Multiple of 7875 and 7880 = 12411000
Step 1: Find the prime factorization of 7875
7875 = 3 x 3 x 5 x 5 x 5 x 7
Step 2: Find the prime factorization of 7880
7880 = 2 x 2 x 2 x 5 x 197
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 12411000 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 7 x 197
Step 4: Therefore, the least common multiple of 7875 and 7880 is 12411000.