Least Common Multiple (LCM) of 69 and 88
The least common multiple (LCM) of 69 and 88 is 6072.
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 88?
First, calculate the GCD of 69 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 88 = 0 remainder 69 |
| 2 | 88 ÷ 69 = 1 remainder 19 |
| 3 | 69 ÷ 19 = 3 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 164 | 27388 |
| 130 and 175 | 4550 |
| 162 and 116 | 9396 |
| 114 and 31 | 3534 |
| 18 and 167 | 3006 |