Least Common Multiple (LCM) of 136 and 83
The least common multiple (LCM) of 136 and 83 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 136 and 83?
First, calculate the GCD of 136 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 83 = 1 remainder 53 |
| 2 | 83 ÷ 53 = 1 remainder 30 |
| 3 | 53 ÷ 30 = 1 remainder 23 |
| 4 | 30 ÷ 23 = 1 remainder 7 |
| 5 | 23 ÷ 7 = 3 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 175 | 14175 |
| 83 and 198 | 16434 |
| 137 and 73 | 10001 |
| 152 and 127 | 19304 |
| 32 and 84 | 672 |