Least Common Multiple (LCM) of 46 and 69
The least common multiple (LCM) of 46 and 69 is 138.
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 69?
First, calculate the GCD of 46 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 69 = 0 remainder 46 |
| 2 | 69 ÷ 46 = 1 remainder 23 |
| 3 | 46 ÷ 23 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 183 | 24339 |
| 133 and 135 | 17955 |
| 34 and 45 | 1530 |
| 109 and 140 | 15260 |
| 151 and 30 | 4530 |