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 |
|---|---|
| 171 and 119 | 20349 |
| 123 and 112 | 13776 |
| 131 and 162 | 21222 |
| 42 and 153 | 2142 |
| 55 and 138 | 7590 |