Least Common Multiple (LCM) of 102 and 169
The least common multiple (LCM) of 102 and 169 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 102 and 169?
First, calculate the GCD of 102 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 169 = 0 remainder 102 |
| 2 | 169 ÷ 102 = 1 remainder 67 |
| 3 | 102 ÷ 67 = 1 remainder 35 |
| 4 | 67 ÷ 35 = 1 remainder 32 |
| 5 | 35 ÷ 32 = 1 remainder 3 |
| 6 | 32 ÷ 3 = 10 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 90 | 3960 |
| 99 and 178 | 17622 |
| 145 and 163 | 23635 |
| 90 and 65 | 1170 |
| 159 and 72 | 3816 |