Least Common Multiple (LCM) of 178 and 67
The least common multiple (LCM) of 178 and 67 is 11926.
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 178 and 67?
First, calculate the GCD of 178 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 67 = 2 remainder 44 |
| 2 | 67 ÷ 44 = 1 remainder 23 |
| 3 | 44 ÷ 23 = 1 remainder 21 |
| 4 | 23 ÷ 21 = 1 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 70 | 2380 |
| 143 and 29 | 4147 |
| 90 and 13 | 1170 |
| 134 and 38 | 2546 |
| 120 and 96 | 480 |