Least Common Multiple (LCM) of 46 and 168
The least common multiple (LCM) of 46 and 168 is 3864.
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 168?
First, calculate the GCD of 46 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 168 = 0 remainder 46 |
| 2 | 168 ÷ 46 = 3 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 |
|---|---|
| 154 and 198 | 1386 |
| 119 and 18 | 2142 |
| 22 and 16 | 176 |
| 184 and 129 | 23736 |
| 108 and 89 | 9612 |