Least Common Multiple (LCM) of 46 and 145
The least common multiple (LCM) of 46 and 145 is 6670.
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 145?
First, calculate the GCD of 46 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 145 = 0 remainder 46 |
| 2 | 145 ÷ 46 = 3 remainder 7 |
| 3 | 46 ÷ 7 = 6 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 105 | 420 |
| 37 and 91 | 3367 |
| 134 and 41 | 5494 |
| 49 and 20 | 980 |
| 109 and 12 | 1308 |