Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2104 and 2107 the smallest integer that is 4433128 that is divisible by both numbers.
Least Common Multiple (LCM) of 2104 and 2107 is 4433128.
LCM(2104,2107) = 4433128
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 2104 and 2107. First we will calculate the prime factors of 2104 and 2107.
Prime Factorization of 2104
2 | 2104 |
2 | 1052 |
2 | 526 |
263 | 263 |
1 |
Prime factors of 2104 are 2,263. Prime factorization of 2104 in exponential form is:
2104 = 23×2631
Prime Factorization of 2107
7 | 2107 |
7 | 301 |
43 | 43 |
1 |
Prime factors of 2107 are 7,43. Prime factorization of 2107 in exponential form is:
2107 = 72×431
Now multiplying the highest exponent prime factors to calculate the LCM of 2104 and 2107.
LCM(2104,2107) = 23×72×431×2631
LCM(2104,2107) = 4433128
Factors of 2104
List of positive integer factors of 2104 that divides 2104 without a remainder.
1, 2, 4, 8, 263, 526, 1052, 2104
Factors of 2107
List of positive integer factors of 2107 that divides 2107 without a remainder.
1, 7, 43, 49, 301, 2107
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2104 and 2107, than apply into the LCM equation.
GCF(2104,2107) = 1
LCM(2104,2107) = ( 2104 × 2107) / 1
LCM(2104,2107) = 4433128 / 1
LCM(2104,2107) = 4433128
(i) The LCM of 2107 and 2104 is associative
LCM of 2104 and 2107 = LCM of 2107 and 2104
1. What is the LCM of 2104 and 2107?
Answer: LCM of 2104 and 2107 is 4433128.
2. What are the Factors of 2104?
Answer: Factors of 2104 are 1, 2, 4, 8, 263, 526, 1052, 2104. There are 8 integers that are factors of 2104. The greatest factor of 2104 is 2104.
3. What are the Factors of 2107?
Answer: Factors of 2107 are 1, 7, 43, 49, 301, 2107. There are 6 integers that are factors of 2107. The greatest factor of 2107 is 2107.
4. How to Find the LCM of 2104 and 2107?
Answer:
Least Common Multiple of 2104 and 2107 = 4433128
Step 1: Find the prime factorization of 2104
2104 = 2 x 2 x 2 x 263
Step 2: Find the prime factorization of 2107
2107 = 7 x 7 x 43
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4433128 = 2 x 2 x 2 x 7 x 7 x 43 x 263
Step 4: Therefore, the least common multiple of 2104 and 2107 is 4433128.