Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2094 and 2100 the smallest integer that is 732900 that is divisible by both numbers.
Least Common Multiple (LCM) of 2094 and 2100 is 732900.
LCM(2094,2100) = 732900
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 2094 and 2100. First we will calculate the prime factors of 2094 and 2100.
Prime Factorization of 2094
2 | 2094 |
3 | 1047 |
349 | 349 |
1 |
Prime factors of 2094 are 2, 3,349. Prime factorization of 2094 in exponential form is:
2094 = 21×31×3491
Prime Factorization of 2100
2 | 2100 |
2 | 1050 |
3 | 525 |
5 | 175 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 2100 are 2, 3, 5,7. Prime factorization of 2100 in exponential form is:
2100 = 22×31×52×71
Now multiplying the highest exponent prime factors to calculate the LCM of 2094 and 2100.
LCM(2094,2100) = 22×31×52×71×3491
LCM(2094,2100) = 732900
Factors of 2094
List of positive integer factors of 2094 that divides 2094 without a remainder.
1, 2, 3, 6, 349, 698, 1047, 2094
Factors of 2100
List of positive integer factors of 2100 that divides 2100 without a remainder.
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2094 and 2100, than apply into the LCM equation.
GCF(2094,2100) = 6
LCM(2094,2100) = ( 2094 × 2100) / 6
LCM(2094,2100) = 4397400 / 6
LCM(2094,2100) = 732900
(i) The LCM of 2100 and 2094 is associative
LCM of 2094 and 2100 = LCM of 2100 and 2094
1. What is the LCM of 2094 and 2100?
Answer: LCM of 2094 and 2100 is 732900.
2. What are the Factors of 2094?
Answer: Factors of 2094 are 1, 2, 3, 6, 349, 698, 1047, 2094. There are 8 integers that are factors of 2094. The greatest factor of 2094 is 2094.
3. What are the Factors of 2100?
Answer: Factors of 2100 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100. There are 36 integers that are factors of 2100. The greatest factor of 2100 is 2100.
4. How to Find the LCM of 2094 and 2100?
Answer:
Least Common Multiple of 2094 and 2100 = 732900
Step 1: Find the prime factorization of 2094
2094 = 2 x 3 x 349
Step 2: Find the prime factorization of 2100
2100 = 2 x 2 x 3 x 5 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 732900 = 2 x 2 x 3 x 5 x 5 x 7 x 349
Step 4: Therefore, the least common multiple of 2094 and 2100 is 732900.