Least Common Multiple (LCM) of 30 and 136
The least common multiple (LCM) of 30 and 136 is 2040.
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 30 and 136?
First, calculate the GCD of 30 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 136 = 0 remainder 30 |
| 2 | 136 ÷ 30 = 4 remainder 16 |
| 3 | 30 ÷ 16 = 1 remainder 14 |
| 4 | 16 ÷ 14 = 1 remainder 2 |
| 5 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 170 | 14110 |
| 22 and 157 | 3454 |
| 188 and 165 | 31020 |
| 150 and 138 | 3450 |
| 109 and 131 | 14279 |