Least Common Multiple (LCM) of 101 and 113
The least common multiple (LCM) of 101 and 113 is 11413.
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 113?
First, calculate the GCD of 101 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 113 = 0 remainder 101 |
| 2 | 113 ÷ 101 = 1 remainder 12 |
| 3 | 101 ÷ 12 = 8 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 91 | 17017 |
| 97 and 12 | 1164 |
| 118 and 108 | 6372 |
| 60 and 97 | 5820 |
| 183 and 183 | 183 |