Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 4100 and 4106 the smallest integer that is 8417300 that is divisible by both numbers.
Least Common Multiple (LCM) of 4100 and 4106 is 8417300.
LCM(4100,4106) = 8417300
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 4100 and 4106. First we will calculate the prime factors of 4100 and 4106.
Prime Factorization of 4100
2 | 4100 |
2 | 2050 |
5 | 1025 |
5 | 205 |
41 | 41 |
1 |
Prime factors of 4100 are 2, 5,41. Prime factorization of 4100 in exponential form is:
4100 = 22×52×411
Prime Factorization of 4106
2 | 4106 |
2053 | 2053 |
1 |
Prime factors of 4106 are 2,2053. Prime factorization of 4106 in exponential form is:
4106 = 21×20531
Now multiplying the highest exponent prime factors to calculate the LCM of 4100 and 4106.
LCM(4100,4106) = 22×52×411×20531
LCM(4100,4106) = 8417300
Factors of 4100
List of positive integer factors of 4100 that divides 4100 without a remainder.
1, 2, 4, 5, 10, 20, 25, 41, 50, 82, 100, 164, 205, 410, 820, 1025, 2050, 4100
Factors of 4106
List of positive integer factors of 4106 that divides 4106 without a remainder.
1, 2, 2053, 4106
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4100 and 4106, than apply into the LCM equation.
GCF(4100,4106) = 2
LCM(4100,4106) = ( 4100 × 4106) / 2
LCM(4100,4106) = 16834600 / 2
LCM(4100,4106) = 8417300
(i) The LCM of 4106 and 4100 is associative
LCM of 4100 and 4106 = LCM of 4106 and 4100
1. What is the LCM of 4100 and 4106?
Answer: LCM of 4100 and 4106 is 8417300.
2. What are the Factors of 4100?
Answer: Factors of 4100 are 1, 2, 4, 5, 10, 20, 25, 41, 50, 82, 100, 164, 205, 410, 820, 1025, 2050, 4100. There are 18 integers that are factors of 4100. The greatest factor of 4100 is 4100.
3. What are the Factors of 4106?
Answer: Factors of 4106 are 1, 2, 2053, 4106. There are 4 integers that are factors of 4106. The greatest factor of 4106 is 4106.
4. How to Find the LCM of 4100 and 4106?
Answer:
Least Common Multiple of 4100 and 4106 = 8417300
Step 1: Find the prime factorization of 4100
4100 = 2 x 2 x 5 x 5 x 41
Step 2: Find the prime factorization of 4106
4106 = 2 x 2053
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 8417300 = 2 x 2 x 5 x 5 x 41 x 2053
Step 4: Therefore, the least common multiple of 4100 and 4106 is 8417300.