Least Common Multiple (LCM) of 178 and 84
The least common multiple (LCM) of 178 and 84 is 7476.
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 84?
First, calculate the GCD of 178 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 84 = 2 remainder 10 |
| 2 | 84 ÷ 10 = 8 remainder 4 |
| 3 | 10 ÷ 4 = 2 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 193 | 20265 |
| 24 and 60 | 120 |
| 58 and 174 | 174 |
| 67 and 100 | 6700 |
| 141 and 52 | 7332 |