Least Common Multiple (LCM) of 46 and 73
The least common multiple (LCM) of 46 and 73 is 3358.
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 73?
First, calculate the GCD of 46 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 73 = 0 remainder 46 |
| 2 | 73 ÷ 46 = 1 remainder 27 |
| 3 | 46 ÷ 27 = 1 remainder 19 |
| 4 | 27 ÷ 19 = 1 remainder 8 |
| 5 | 19 ÷ 8 = 2 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 54 | 2322 |
| 132 and 198 | 396 |
| 121 and 77 | 847 |
| 70 and 42 | 210 |
| 85 and 90 | 1530 |