Least Common Multiple (LCM) of 150 and 169
The least common multiple (LCM) of 150 and 169 is 25350.
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 150 and 169?
First, calculate the GCD of 150 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 169 = 0 remainder 150 |
| 2 | 169 ÷ 150 = 1 remainder 19 |
| 3 | 150 ÷ 19 = 7 remainder 17 |
| 4 | 19 ÷ 17 = 1 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 123 | 13899 |
| 93 and 186 | 186 |
| 77 and 25 | 1925 |
| 127 and 183 | 23241 |
| 147 and 16 | 2352 |