Least Common Multiple (LCM) of 83 and 136
The least common multiple (LCM) of 83 and 136 is 11288.
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 83 and 136?
First, calculate the GCD of 83 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 136 = 0 remainder 83 |
| 2 | 136 ÷ 83 = 1 remainder 53 |
| 3 | 83 ÷ 53 = 1 remainder 30 |
| 4 | 53 ÷ 30 = 1 remainder 23 |
| 5 | 30 ÷ 23 = 1 remainder 7 |
| 6 | 23 ÷ 7 = 3 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 62 | 11594 |
| 113 and 33 | 3729 |
| 108 and 167 | 18036 |
| 65 and 162 | 10530 |
| 173 and 53 | 9169 |