Least Common Multiple (LCM) of 135 and 74
The least common multiple (LCM) of 135 and 74 is 9990.
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 135 and 74?
First, calculate the GCD of 135 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 74 = 1 remainder 61 |
| 2 | 74 ÷ 61 = 1 remainder 13 |
| 3 | 61 ÷ 13 = 4 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 76 | 1900 |
| 102 and 138 | 2346 |
| 23 and 24 | 552 |
| 167 and 77 | 12859 |
| 196 and 158 | 15484 |