Least Common Multiple (LCM) of 67 and 176
The least common multiple (LCM) of 67 and 176 is 11792.
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 67 and 176?
First, calculate the GCD of 67 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 176 = 0 remainder 67 |
| 2 | 176 ÷ 67 = 2 remainder 42 |
| 3 | 67 ÷ 42 = 1 remainder 25 |
| 4 | 42 ÷ 25 = 1 remainder 17 |
| 5 | 25 ÷ 17 = 1 remainder 8 |
| 6 | 17 ÷ 8 = 2 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 104 | 1768 |
| 20 and 155 | 620 |
| 46 and 115 | 230 |
| 50 and 162 | 4050 |
| 123 and 92 | 11316 |