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 |
|---|---|
| 185 and 151 | 27935 |
| 21 and 185 | 3885 |
| 108 and 106 | 5724 |
| 171 and 137 | 23427 |
| 52 and 195 | 780 |