Least Common Multiple (LCM) of 117 and 151
The least common multiple (LCM) of 117 and 151 is 17667.
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 117 and 151?
First, calculate the GCD of 117 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 151 = 0 remainder 117 |
| 2 | 151 ÷ 117 = 1 remainder 34 |
| 3 | 117 ÷ 34 = 3 remainder 15 |
| 4 | 34 ÷ 15 = 2 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 141 | 9447 |
| 109 and 31 | 3379 |
| 172 and 45 | 7740 |
| 49 and 82 | 4018 |
| 43 and 40 | 1720 |