Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2101 and 2104 the smallest integer that is 4420504 that is divisible by both numbers.
Least Common Multiple (LCM) of 2101 and 2104 is 4420504.
LCM(2101,2104) = 4420504
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 2101 and 2104. First we will calculate the prime factors of 2101 and 2104.
Prime Factorization of 2101
11 | 2101 |
191 | 191 |
1 |
Prime factors of 2101 are 11,191. Prime factorization of 2101 in exponential form is:
2101 = 111×1911
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
Now multiplying the highest exponent prime factors to calculate the LCM of 2101 and 2104.
LCM(2101,2104) = 23×111×1911×2631
LCM(2101,2104) = 4420504
Factors of 2101
List of positive integer factors of 2101 that divides 2101 without a remainder.
1, 11, 191, 2101
Factors of 2104
List of positive integer factors of 2104 that divides 2104 without a remainder.
1, 2, 4, 8, 263, 526, 1052, 2104
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2101 and 2104, than apply into the LCM equation.
GCF(2101,2104) = 1
LCM(2101,2104) = ( 2101 × 2104) / 1
LCM(2101,2104) = 4420504 / 1
LCM(2101,2104) = 4420504
(i) The LCM of 2104 and 2101 is associative
LCM of 2101 and 2104 = LCM of 2104 and 2101
1. What is the LCM of 2101 and 2104?
Answer: LCM of 2101 and 2104 is 4420504.
2. What are the Factors of 2101?
Answer: Factors of 2101 are 1, 11, 191, 2101. There are 4 integers that are factors of 2101. The greatest factor of 2101 is 2101.
3. 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.
4. How to Find the LCM of 2101 and 2104?
Answer:
Least Common Multiple of 2101 and 2104 = 4420504
Step 1: Find the prime factorization of 2101
2101 = 11 x 191
Step 2: Find the prime factorization of 2104
2104 = 2 x 2 x 2 x 263
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4420504 = 2 x 2 x 2 x 11 x 191 x 263
Step 4: Therefore, the least common multiple of 2101 and 2104 is 4420504.