Least Common Multiple (LCM) of 101 and 118
The least common multiple (LCM) of 101 and 118 is 11918.
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 118?
First, calculate the GCD of 101 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 118 = 0 remainder 101 |
| 2 | 118 ÷ 101 = 1 remainder 17 |
| 3 | 101 ÷ 17 = 5 remainder 16 |
| 4 | 17 ÷ 16 = 1 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 127 | 13589 |
| 140 and 128 | 4480 |
| 175 and 107 | 18725 |
| 98 and 48 | 2352 |
| 128 and 138 | 8832 |