Least Common Multiple (LCM) of 46 and 59
The least common multiple (LCM) of 46 and 59 is 2714.
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 59?
First, calculate the GCD of 46 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 59 = 0 remainder 46 |
| 2 | 59 ÷ 46 = 1 remainder 13 |
| 3 | 46 ÷ 13 = 3 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 89 | 3115 |
| 150 and 180 | 900 |
| 124 and 164 | 5084 |
| 183 and 77 | 14091 |
| 133 and 131 | 17423 |