Least Common Multiple (LCM) of 178 and 40
The least common multiple (LCM) of 178 and 40 is 3560.
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 40?
First, calculate the GCD of 178 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 40 = 4 remainder 18 |
| 2 | 40 ÷ 18 = 2 remainder 4 |
| 3 | 18 ÷ 4 = 4 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 106 | 9646 |
| 112 and 88 | 1232 |
| 119 and 128 | 15232 |
| 174 and 114 | 3306 |
| 174 and 164 | 14268 |