Least Common Multiple (LCM) of 119 and 178
The least common multiple (LCM) of 119 and 178 is 21182.
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 119 and 178?
First, calculate the GCD of 119 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 178 = 0 remainder 119 |
| 2 | 178 ÷ 119 = 1 remainder 59 |
| 3 | 119 ÷ 59 = 2 remainder 1 |
| 4 | 59 ÷ 1 = 59 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 177 | 27258 |
| 82 and 140 | 5740 |
| 63 and 30 | 630 |
| 160 and 161 | 25760 |
| 17 and 139 | 2363 |