Least Common Multiple (LCM) of 60 and 97
The least common multiple (LCM) of 60 and 97 is 5820.
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 60 and 97?
First, calculate the GCD of 60 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 97 = 0 remainder 60 |
| 2 | 97 ÷ 60 = 1 remainder 37 |
| 3 | 60 ÷ 37 = 1 remainder 23 |
| 4 | 37 ÷ 23 = 1 remainder 14 |
| 5 | 23 ÷ 14 = 1 remainder 9 |
| 6 | 14 ÷ 9 = 1 remainder 5 |
| 7 | 9 ÷ 5 = 1 remainder 4 |
| 8 | 5 ÷ 4 = 1 remainder 1 |
| 9 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 109 | 15478 |
| 153 and 183 | 9333 |
| 128 and 87 | 11136 |
| 140 and 77 | 1540 |
| 129 and 114 | 4902 |