Least Common Multiple (LCM) of 136 and 52
The least common multiple (LCM) of 136 and 52 is 1768.
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 52?
First, calculate the GCD of 136 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 52 = 2 remainder 32 |
| 2 | 52 ÷ 32 = 1 remainder 20 |
| 3 | 32 ÷ 20 = 1 remainder 12 |
| 4 | 20 ÷ 12 = 1 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 102 | 816 |
| 61 and 28 | 1708 |
| 112 and 34 | 1904 |
| 188 and 102 | 9588 |
| 172 and 25 | 4300 |