Least Common Multiple (LCM) of 101 and 115
The least common multiple (LCM) of 101 and 115 is 11615.
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 101 and 115?
First, calculate the GCD of 101 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 115 = 0 remainder 101 |
| 2 | 115 ÷ 101 = 1 remainder 14 |
| 3 | 101 ÷ 14 = 7 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 137 | 23975 |
| 115 and 69 | 345 |
| 142 and 118 | 8378 |
| 43 and 48 | 2064 |
| 113 and 27 | 3051 |