Least Common Multiple (LCM) of 115 and 21
The least common multiple (LCM) of 115 and 21 is 2415.
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 115 and 21?
First, calculate the GCD of 115 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 21 = 5 remainder 10 |
| 2 | 21 ÷ 10 = 2 remainder 1 |
| 3 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 153 | 5355 |
| 126 and 72 | 504 |
| 113 and 83 | 9379 |
| 68 and 181 | 12308 |
| 123 and 70 | 8610 |