Least Common Multiple (LCM) of 136 and 172
The least common multiple (LCM) of 136 and 172 is 5848.
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 172?
First, calculate the GCD of 136 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 172 = 0 remainder 136 |
| 2 | 172 ÷ 136 = 1 remainder 36 |
| 3 | 136 ÷ 36 = 3 remainder 28 |
| 4 | 36 ÷ 28 = 1 remainder 8 |
| 5 | 28 ÷ 8 = 3 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 47 | 5264 |
| 189 and 192 | 12096 |
| 31 and 50 | 1550 |
| 61 and 62 | 3782 |
| 133 and 181 | 24073 |