Least Common Multiple (LCM) of 10 and 136
The least common multiple (LCM) of 10 and 136 is 680.
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 10 and 136?
First, calculate the GCD of 10 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 136 = 0 remainder 10 |
| 2 | 136 ÷ 10 = 13 remainder 6 |
| 3 | 10 ÷ 6 = 1 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 21 | 147 |
| 130 and 85 | 2210 |
| 48 and 12 | 48 |
| 174 and 113 | 19662 |
| 188 and 188 | 188 |