Least Common Multiple (LCM) of 105 and 136
The least common multiple (LCM) of 105 and 136 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 105 and 136?
First, calculate the GCD of 105 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 136 = 0 remainder 105 |
| 2 | 136 ÷ 105 = 1 remainder 31 |
| 3 | 105 ÷ 31 = 3 remainder 12 |
| 4 | 31 ÷ 12 = 2 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 91 | 728 |
| 110 and 119 | 13090 |
| 69 and 144 | 3312 |
| 45 and 144 | 720 |
| 14 and 57 | 798 |