Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8378 and 8380 the smallest integer that is 35103820 that is divisible by both numbers.
Least Common Multiple (LCM) of 8378 and 8380 is 35103820.
LCM(8378,8380) = 35103820
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 8378 and 8380. First we will calculate the prime factors of 8378 and 8380.
Prime Factorization of 8378
2 | 8378 |
59 | 4189 |
71 | 71 |
1 |
Prime factors of 8378 are 2, 59,71. Prime factorization of 8378 in exponential form is:
8378 = 21×591×711
Prime Factorization of 8380
2 | 8380 |
2 | 4190 |
5 | 2095 |
419 | 419 |
1 |
Prime factors of 8380 are 2, 5,419. Prime factorization of 8380 in exponential form is:
8380 = 22×51×4191
Now multiplying the highest exponent prime factors to calculate the LCM of 8378 and 8380.
LCM(8378,8380) = 22×51×591×711×4191
LCM(8378,8380) = 35103820
Factors of 8378
List of positive integer factors of 8378 that divides 8378 without a remainder.
1, 2, 59, 71, 118, 142, 4189, 8378
Factors of 8380
List of positive integer factors of 8380 that divides 8380 without a remainder.
1, 2, 4, 5, 10, 20, 419, 838, 1676, 2095, 4190, 8380
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8378 and 8380, than apply into the LCM equation.
GCF(8378,8380) = 2
LCM(8378,8380) = ( 8378 × 8380) / 2
LCM(8378,8380) = 70207640 / 2
LCM(8378,8380) = 35103820
(i) The LCM of 8380 and 8378 is associative
LCM of 8378 and 8380 = LCM of 8380 and 8378
1. What is the LCM of 8378 and 8380?
Answer: LCM of 8378 and 8380 is 35103820.
2. What are the Factors of 8378?
Answer: Factors of 8378 are 1, 2, 59, 71, 118, 142, 4189, 8378. There are 8 integers that are factors of 8378. The greatest factor of 8378 is 8378.
3. What are the Factors of 8380?
Answer: Factors of 8380 are 1, 2, 4, 5, 10, 20, 419, 838, 1676, 2095, 4190, 8380. There are 12 integers that are factors of 8380. The greatest factor of 8380 is 8380.
4. How to Find the LCM of 8378 and 8380?
Answer:
Least Common Multiple of 8378 and 8380 = 35103820
Step 1: Find the prime factorization of 8378
8378 = 2 x 59 x 71
Step 2: Find the prime factorization of 8380
8380 = 2 x 2 x 5 x 419
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 35103820 = 2 x 2 x 5 x 59 x 71 x 419
Step 4: Therefore, the least common multiple of 8378 and 8380 is 35103820.