Least Common Multiple (LCM) of 169 and 102
The least common multiple (LCM) of 169 and 102 is 17238.
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 169 and 102?
First, calculate the GCD of 169 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 102 = 1 remainder 67 |
| 2 | 102 ÷ 67 = 1 remainder 35 |
| 3 | 67 ÷ 35 = 1 remainder 32 |
| 4 | 35 ÷ 32 = 1 remainder 3 |
| 5 | 32 ÷ 3 = 10 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 185 | 23680 |
| 25 and 28 | 700 |
| 53 and 120 | 6360 |
| 150 and 53 | 7950 |
| 195 and 168 | 10920 |