Least Common Multiple (LCM) of 21 and 115
The least common multiple (LCM) of 21 and 115 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 21 and 115?
First, calculate the GCD of 21 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 115 = 0 remainder 21 |
| 2 | 115 ÷ 21 = 5 remainder 10 |
| 3 | 21 ÷ 10 = 2 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 158 | 15168 |
| 22 and 200 | 2200 |
| 176 and 111 | 19536 |
| 118 and 142 | 8378 |
| 179 and 132 | 23628 |