Least Common Multiple (LCM) of 69 and 178
The least common multiple (LCM) of 69 and 178 is 12282.
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 69 and 178?
First, calculate the GCD of 69 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 178 = 0 remainder 69 |
| 2 | 178 ÷ 69 = 2 remainder 40 |
| 3 | 69 ÷ 40 = 1 remainder 29 |
| 4 | 40 ÷ 29 = 1 remainder 11 |
| 5 | 29 ÷ 11 = 2 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 97 | 4753 |
| 53 and 83 | 4399 |
| 33 and 50 | 1650 |
| 165 and 114 | 6270 |
| 135 and 105 | 945 |