Least Common Multiple (LCM) of 101 and 116
The least common multiple (LCM) of 101 and 116 is 11716.
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 116?
First, calculate the GCD of 101 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 116 = 0 remainder 101 |
| 2 | 116 ÷ 101 = 1 remainder 15 |
| 3 | 101 ÷ 15 = 6 remainder 11 |
| 4 | 15 ÷ 11 = 1 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 197 | 5319 |
| 123 and 138 | 5658 |
| 63 and 134 | 8442 |
| 163 and 67 | 10921 |
| 177 and 132 | 7788 |