Least Common Multiple (LCM) of 46 and 52
The least common multiple (LCM) of 46 and 52 is 1196.
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 52?
First, calculate the GCD of 46 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 52 = 0 remainder 46 |
| 2 | 52 ÷ 46 = 1 remainder 6 |
| 3 | 46 ÷ 6 = 7 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 112 | 2800 |
| 12 and 112 | 336 |
| 172 and 28 | 1204 |
| 47 and 74 | 3478 |
| 195 and 163 | 31785 |