Least Common Multiple (LCM) of 69 and 157
The least common multiple (LCM) of 69 and 157 is 10833.
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 157?
First, calculate the GCD of 69 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 157 = 0 remainder 69 |
| 2 | 157 ÷ 69 = 2 remainder 19 |
| 3 | 69 ÷ 19 = 3 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 21 | 147 |
| 114 and 138 | 2622 |
| 183 and 193 | 35319 |
| 178 and 71 | 12638 |
| 12 and 22 | 132 |