Least Common Multiple (LCM) of 46 and 133
The least common multiple (LCM) of 46 and 133 is 6118.
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 133?
First, calculate the GCD of 46 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 133 = 0 remainder 46 |
| 2 | 133 ÷ 46 = 2 remainder 41 |
| 3 | 46 ÷ 41 = 1 remainder 5 |
| 4 | 41 ÷ 5 = 8 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 112 | 2128 |
| 107 and 12 | 1284 |
| 35 and 37 | 1295 |
| 15 and 181 | 2715 |
| 69 and 87 | 2001 |