Least Common Multiple (LCM) of 46 and 76
The least common multiple (LCM) of 46 and 76 is 1748.
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 76?
First, calculate the GCD of 46 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 76 = 0 remainder 46 |
| 2 | 76 ÷ 46 = 1 remainder 30 |
| 3 | 46 ÷ 30 = 1 remainder 16 |
| 4 | 30 ÷ 16 = 1 remainder 14 |
| 5 | 16 ÷ 14 = 1 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 18 | 180 |
| 139 and 138 | 19182 |
| 35 and 17 | 595 |
| 17 and 39 | 663 |
| 83 and 39 | 3237 |