Least Common Multiple (LCM) of 100 and 115
The least common multiple (LCM) of 100 and 115 is 2300.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 100 and 115?
First, calculate the GCD of 100 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 115 = 0 remainder 100 |
| 2 | 115 ÷ 100 = 1 remainder 15 |
| 3 | 100 ÷ 15 = 6 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 122 | 5124 |
| 29 and 98 | 2842 |
| 139 and 95 | 13205 |
| 137 and 75 | 10275 |
| 112 and 60 | 1680 |