Least Common Multiple (LCM) of 101 and 117
The least common multiple (LCM) of 101 and 117 is 11817.
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 117?
First, calculate the GCD of 101 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 117 = 0 remainder 101 |
| 2 | 117 ÷ 101 = 1 remainder 16 |
| 3 | 101 ÷ 16 = 6 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 27 | 1026 |
| 128 and 60 | 1920 |
| 43 and 162 | 6966 |
| 47 and 23 | 1081 |
| 105 and 121 | 12705 |