Least Common Multiple (LCM) of 46 and 135
The least common multiple (LCM) of 46 and 135 is 6210.
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 46 and 135?
First, calculate the GCD of 46 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 135 = 0 remainder 46 |
| 2 | 135 ÷ 46 = 2 remainder 43 |
| 3 | 46 ÷ 43 = 1 remainder 3 |
| 4 | 43 ÷ 3 = 14 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 52 | 2652 |
| 128 and 158 | 10112 |
| 180 and 165 | 1980 |
| 59 and 32 | 1888 |
| 115 and 78 | 8970 |