Least Common Multiple (LCM) of 69 and 167
The least common multiple (LCM) of 69 and 167 is 11523.
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 167?
First, calculate the GCD of 69 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 167 = 0 remainder 69 |
| 2 | 167 ÷ 69 = 2 remainder 29 |
| 3 | 69 ÷ 29 = 2 remainder 11 |
| 4 | 29 ÷ 11 = 2 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 91 | 1456 |
| 160 and 20 | 160 |
| 13 and 91 | 91 |
| 122 and 109 | 13298 |
| 116 and 156 | 4524 |