Least Common Multiple (LCM) of 101 and 169
The least common multiple (LCM) of 101 and 169 is 17069.
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 101 and 169?
First, calculate the GCD of 101 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 169 = 0 remainder 101 |
| 2 | 169 ÷ 101 = 1 remainder 68 |
| 3 | 101 ÷ 68 = 1 remainder 33 |
| 4 | 68 ÷ 33 = 2 remainder 2 |
| 5 | 33 ÷ 2 = 16 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 118 | 14042 |
| 90 and 86 | 3870 |
| 50 and 105 | 1050 |
| 66 and 45 | 990 |
| 189 and 113 | 21357 |