Least Common Multiple (LCM) of 49 and 135
The least common multiple (LCM) of 49 and 135 is 6615.
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 49 and 135?
First, calculate the GCD of 49 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 135 = 0 remainder 49 |
| 2 | 135 ÷ 49 = 2 remainder 37 |
| 3 | 49 ÷ 37 = 1 remainder 12 |
| 4 | 37 ÷ 12 = 3 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 85 | 5355 |
| 33 and 21 | 231 |
| 114 and 181 | 20634 |
| 47 and 45 | 2115 |
| 113 and 172 | 19436 |