Least Common Multiple (LCM) of 69 and 150
The least common multiple (LCM) of 69 and 150 is 3450.
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 69 and 150?
First, calculate the GCD of 69 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 150 = 0 remainder 69 |
| 2 | 150 ÷ 69 = 2 remainder 12 |
| 3 | 69 ÷ 12 = 5 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 111 | 6660 |
| 79 and 35 | 2765 |
| 60 and 193 | 11580 |
| 116 and 118 | 6844 |
| 149 and 48 | 7152 |