Least Common Multiple (LCM) of 178 and 106
The least common multiple (LCM) of 178 and 106 is 9434.
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 106?
First, calculate the GCD of 178 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 106 = 1 remainder 72 |
| 2 | 106 ÷ 72 = 1 remainder 34 |
| 3 | 72 ÷ 34 = 2 remainder 4 |
| 4 | 34 ÷ 4 = 8 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 38 | 6954 |
| 161 and 10 | 1610 |
| 13 and 135 | 1755 |
| 181 and 152 | 27512 |
| 152 and 118 | 8968 |