Least Common Multiple (LCM) of 69 and 188
The least common multiple (LCM) of 69 and 188 is 12972.
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 188?
First, calculate the GCD of 69 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 188 = 0 remainder 69 |
| 2 | 188 ÷ 69 = 2 remainder 50 |
| 3 | 69 ÷ 50 = 1 remainder 19 |
| 4 | 50 ÷ 19 = 2 remainder 12 |
| 5 | 19 ÷ 12 = 1 remainder 7 |
| 6 | 12 ÷ 7 = 1 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 35 | 1610 |
| 170 and 90 | 1530 |
| 100 and 126 | 6300 |
| 105 and 144 | 5040 |
| 14 and 88 | 616 |