Least Common Multiple (LCM) of 178 and 72
The least common multiple (LCM) of 178 and 72 is 6408.
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 72?
First, calculate the GCD of 178 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 72 = 2 remainder 34 |
| 2 | 72 ÷ 34 = 2 remainder 4 |
| 3 | 34 ÷ 4 = 8 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 17 | 1292 |
| 96 and 142 | 6816 |
| 42 and 50 | 1050 |
| 112 and 160 | 1120 |
| 140 and 39 | 5460 |