Least Common Multiple (LCM) of 136 and 105
The least common multiple (LCM) of 136 and 105 is 14280.
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 105?
First, calculate the GCD of 136 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 105 = 1 remainder 31 |
| 2 | 105 ÷ 31 = 3 remainder 12 |
| 3 | 31 ÷ 12 = 2 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 61 | 7625 |
| 30 and 37 | 1110 |
| 101 and 57 | 5757 |
| 75 and 172 | 12900 |
| 145 and 133 | 19285 |