Least Common Multiple (LCM) of 46 and 65
The least common multiple (LCM) of 46 and 65 is 2990.
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 65?
First, calculate the GCD of 46 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 65 = 0 remainder 46 |
| 2 | 65 ÷ 46 = 1 remainder 19 |
| 3 | 46 ÷ 19 = 2 remainder 8 |
| 4 | 19 ÷ 8 = 2 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 198 | 38214 |
| 81 and 185 | 14985 |
| 140 and 26 | 1820 |
| 194 and 191 | 37054 |
| 35 and 118 | 4130 |