Least Common Multiple (LCM) of 106 and 136
The least common multiple (LCM) of 106 and 136 is 7208.
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 106 and 136?
First, calculate the GCD of 106 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 136 = 0 remainder 106 |
| 2 | 136 ÷ 106 = 1 remainder 30 |
| 3 | 106 ÷ 30 = 3 remainder 16 |
| 4 | 30 ÷ 16 = 1 remainder 14 |
| 5 | 16 ÷ 14 = 1 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 100 | 1300 |
| 57 and 200 | 11400 |
| 200 and 92 | 4600 |
| 110 and 38 | 2090 |
| 112 and 25 | 2800 |