Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2380 and 2384 the smallest integer that is 1418480 that is divisible by both numbers.
Least Common Multiple (LCM) of 2380 and 2384 is 1418480.
LCM(2380,2384) = 1418480
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 2380 and 2384. First we will calculate the prime factors of 2380 and 2384.
Prime Factorization of 2380
2 | 2380 |
2 | 1190 |
5 | 595 |
7 | 119 |
17 | 17 |
1 |
Prime factors of 2380 are 2, 5, 7,17. Prime factorization of 2380 in exponential form is:
2380 = 22×51×71×171
Prime Factorization of 2384
2 | 2384 |
2 | 1192 |
2 | 596 |
2 | 298 |
149 | 149 |
1 |
Prime factors of 2384 are 2,149. Prime factorization of 2384 in exponential form is:
2384 = 24×1491
Now multiplying the highest exponent prime factors to calculate the LCM of 2380 and 2384.
LCM(2380,2384) = 24×51×71×171×1491
LCM(2380,2384) = 1418480
Factors of 2380
List of positive integer factors of 2380 that divides 2380 without a remainder.
1, 2, 4, 5, 7, 10, 14, 17, 20, 28, 34, 35, 68, 70, 85, 119, 140, 170, 238, 340, 476, 595, 1190, 2380
Factors of 2384
List of positive integer factors of 2384 that divides 2384 without a remainder.
1, 2, 4, 8, 16, 149, 298, 596, 1192, 2384
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2380 and 2384, than apply into the LCM equation.
GCF(2380,2384) = 4
LCM(2380,2384) = ( 2380 × 2384) / 4
LCM(2380,2384) = 5673920 / 4
LCM(2380,2384) = 1418480
(i) The LCM of 2384 and 2380 is associative
LCM of 2380 and 2384 = LCM of 2384 and 2380
1. What is the LCM of 2380 and 2384?
Answer: LCM of 2380 and 2384 is 1418480.
2. What are the Factors of 2380?
Answer: Factors of 2380 are 1, 2, 4, 5, 7, 10, 14, 17, 20, 28, 34, 35, 68, 70, 85, 119, 140, 170, 238, 340, 476, 595, 1190, 2380. There are 24 integers that are factors of 2380. The greatest factor of 2380 is 2380.
3. What are the Factors of 2384?
Answer: Factors of 2384 are 1, 2, 4, 8, 16, 149, 298, 596, 1192, 2384. There are 10 integers that are factors of 2384. The greatest factor of 2384 is 2384.
4. How to Find the LCM of 2380 and 2384?
Answer:
Least Common Multiple of 2380 and 2384 = 1418480
Step 1: Find the prime factorization of 2380
2380 = 2 x 2 x 5 x 7 x 17
Step 2: Find the prime factorization of 2384
2384 = 2 x 2 x 2 x 2 x 149
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1418480 = 2 x 2 x 2 x 2 x 5 x 7 x 17 x 149
Step 4: Therefore, the least common multiple of 2380 and 2384 is 1418480.