Least Common Multiple (LCM) of 90 and 169
The least common multiple (LCM) of 90 and 169 is 15210.
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 90 and 169?
First, calculate the GCD of 90 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 169 = 0 remainder 90 |
| 2 | 169 ÷ 90 = 1 remainder 79 |
| 3 | 90 ÷ 79 = 1 remainder 11 |
| 4 | 79 ÷ 11 = 7 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 104 | 2184 |
| 143 and 103 | 14729 |
| 194 and 20 | 1940 |
| 40 and 65 | 520 |
| 111 and 169 | 18759 |