Least Common Multiple (LCM) of 135 and 98
The least common multiple (LCM) of 135 and 98 is 13230.
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 98?
First, calculate the GCD of 135 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 98 = 1 remainder 37 |
| 2 | 98 ÷ 37 = 2 remainder 24 |
| 3 | 37 ÷ 24 = 1 remainder 13 |
| 4 | 24 ÷ 13 = 1 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 100 | 300 |
| 174 and 45 | 2610 |
| 111 and 38 | 4218 |
| 40 and 99 | 3960 |
| 117 and 85 | 9945 |