Least Common Multiple (LCM) of 69 and 106
The least common multiple (LCM) of 69 and 106 is 7314.
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 106?
First, calculate the GCD of 69 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 106 = 0 remainder 69 |
| 2 | 106 ÷ 69 = 1 remainder 37 |
| 3 | 69 ÷ 37 = 1 remainder 32 |
| 4 | 37 ÷ 32 = 1 remainder 5 |
| 5 | 32 ÷ 5 = 6 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 23 | 1449 |
| 49 and 76 | 3724 |
| 126 and 93 | 3906 |
| 114 and 121 | 13794 |
| 98 and 84 | 588 |