Least Common Multiple (LCM) of 112 and 178
The least common multiple (LCM) of 112 and 178 is 9968.
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 112 and 178?
First, calculate the GCD of 112 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 178 = 0 remainder 112 |
| 2 | 178 ÷ 112 = 1 remainder 66 |
| 3 | 112 ÷ 66 = 1 remainder 46 |
| 4 | 66 ÷ 46 = 1 remainder 20 |
| 5 | 46 ÷ 20 = 2 remainder 6 |
| 6 | 20 ÷ 6 = 3 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 90 | 630 |
| 62 and 103 | 6386 |
| 49 and 200 | 9800 |
| 145 and 69 | 10005 |
| 145 and 50 | 1450 |