Least Common Multiple (LCM) of 46 and 122
The least common multiple (LCM) of 46 and 122 is 2806.
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 122?
First, calculate the GCD of 46 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 122 = 0 remainder 46 |
| 2 | 122 ÷ 46 = 2 remainder 30 |
| 3 | 46 ÷ 30 = 1 remainder 16 |
| 4 | 30 ÷ 16 = 1 remainder 14 |
| 5 | 16 ÷ 14 = 1 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 43 | 8428 |
| 135 and 180 | 540 |
| 148 and 88 | 3256 |
| 156 and 140 | 5460 |
| 93 and 30 | 930 |