Least Common Multiple (LCM) of 69 and 101
The least common multiple (LCM) of 69 and 101 is 6969.
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 101?
First, calculate the GCD of 69 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 101 = 0 remainder 69 |
| 2 | 101 ÷ 69 = 1 remainder 32 |
| 3 | 69 ÷ 32 = 2 remainder 5 |
| 4 | 32 ÷ 5 = 6 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 66 | 462 |
| 70 and 195 | 2730 |
| 173 and 151 | 26123 |
| 193 and 99 | 19107 |
| 122 and 12 | 732 |