Least Common Multiple (LCM) of 178 and 110
The least common multiple (LCM) of 178 and 110 is 9790.
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 110?
First, calculate the GCD of 178 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 110 = 1 remainder 68 |
| 2 | 110 ÷ 68 = 1 remainder 42 |
| 3 | 68 ÷ 42 = 1 remainder 26 |
| 4 | 42 ÷ 26 = 1 remainder 16 |
| 5 | 26 ÷ 16 = 1 remainder 10 |
| 6 | 16 ÷ 10 = 1 remainder 6 |
| 7 | 10 ÷ 6 = 1 remainder 4 |
| 8 | 6 ÷ 4 = 1 remainder 2 |
| 9 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 112 | 5040 |
| 32 and 30 | 480 |
| 143 and 166 | 23738 |
| 120 and 45 | 360 |
| 34 and 70 | 1190 |