Least Common Multiple (LCM) of 100 and 15
The least common multiple (LCM) of 100 and 15 is 300.
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 15?
First, calculate the GCD of 100 and 15 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 15 = 6 remainder 10 |
| 2 | 15 ÷ 10 = 1 remainder 5 |
| 3 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 22 | 1914 |
| 200 and 99 | 19800 |
| 179 and 43 | 7697 |
| 130 and 37 | 4810 |
| 101 and 27 | 2727 |