Least Common Multiple (LCM) of 46 and 167
The least common multiple (LCM) of 46 and 167 is 7682.
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 167?
First, calculate the GCD of 46 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 167 = 0 remainder 46 |
| 2 | 167 ÷ 46 = 3 remainder 29 |
| 3 | 46 ÷ 29 = 1 remainder 17 |
| 4 | 29 ÷ 17 = 1 remainder 12 |
| 5 | 17 ÷ 12 = 1 remainder 5 |
| 6 | 12 ÷ 5 = 2 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 124 | 16988 |
| 72 and 122 | 4392 |
| 96 and 150 | 2400 |
| 184 and 32 | 736 |
| 112 and 100 | 2800 |