Least Common Multiple (LCM) of 73 and 167
The least common multiple (LCM) of 73 and 167 is 12191.
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 73 and 167?
First, calculate the GCD of 73 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 167 = 0 remainder 73 |
| 2 | 167 ÷ 73 = 2 remainder 21 |
| 3 | 73 ÷ 21 = 3 remainder 10 |
| 4 | 21 ÷ 10 = 2 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 129 | 1290 |
| 51 and 191 | 9741 |
| 88 and 13 | 1144 |
| 32 and 101 | 3232 |
| 112 and 194 | 10864 |