Least Common Multiple (LCM) of 136 and 101
The least common multiple (LCM) of 136 and 101 is 13736.
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 101?
First, calculate the GCD of 136 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 101 = 1 remainder 35 |
| 2 | 101 ÷ 35 = 2 remainder 31 |
| 3 | 35 ÷ 31 = 1 remainder 4 |
| 4 | 31 ÷ 4 = 7 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 111 | 1887 |
| 40 and 77 | 3080 |
| 189 and 72 | 1512 |
| 118 and 188 | 11092 |
| 121 and 78 | 9438 |