Least Common Multiple (LCM) of 75 and 136
The least common multiple (LCM) of 75 and 136 is 10200.
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 75 and 136?
First, calculate the GCD of 75 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 136 = 0 remainder 75 |
| 2 | 136 ÷ 75 = 1 remainder 61 |
| 3 | 75 ÷ 61 = 1 remainder 14 |
| 4 | 61 ÷ 14 = 4 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 143 | 1430 |
| 196 and 78 | 7644 |
| 165 and 36 | 1980 |
| 121 and 115 | 13915 |
| 68 and 107 | 7276 |