Least Common Multiple (LCM) of 169 and 103
The least common multiple (LCM) of 169 and 103 is 17407.
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 103?
First, calculate the GCD of 169 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 103 = 1 remainder 66 |
| 2 | 103 ÷ 66 = 1 remainder 37 |
| 3 | 66 ÷ 37 = 1 remainder 29 |
| 4 | 37 ÷ 29 = 1 remainder 8 |
| 5 | 29 ÷ 8 = 3 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 36 | 5148 |
| 70 and 168 | 840 |
| 162 and 192 | 5184 |
| 171 and 122 | 20862 |
| 132 and 76 | 2508 |