Bob's frog can travel 6 inches per jump, Kim's frog can travel 9 inches, and Jack's frog can travel 13 inches. If the three frogs start off at point 0 inches, how many inches will it be to the next point that all three frogs touch?
To find the next point that all three frogs touch, we need to find the least common multiple (LCM) of their jumping distances.
The LCM of 6, 9, and 13 can be found by listing the multiples of each number until we find a common multiple:
Multiples of 6: 6, 12, 18, 24, 30, ...
Multiples of 9: 9, 18, 27, 36, ...
Multiples of 13: 13, 26, 39, ...
From the lists above, we can see that the least common multiple of 6, 9, and 13 is 18.
Therefore, the next point that all three frogs touch is 18 inches away from the starting point.
To find the next point that all three frogs touch, we need to find the least common multiple (LCM) of their travel distances, which in this case are 6, 9, and 13 inches.
To find the LCM of these three numbers, we can follow these steps:
Step 1: Prime factorize each number.
- 6 = 2 * 3
- 9 = 3 * 3
- 13 is already a prime number, so it remains as it is.
Step 2: Identify the highest power for each prime factor.
- 2 * 3^2 * 13
Step 3: Multiply the prime factors raised to their highest powers.
- 2 * 3^2 * 13 = 78
Therefore, the LCM of 6, 9, and 13 is 78 inches.
Hence, the next point that all three frogs touch will be at a distance of 78 inches.
draw it. Start at 0, then + 9 for Kim. +13 for jack, and + 6 for Bob. Contuine you this till you find where they meet
You are actually just finding the LCM of 6, 9, and 13
which is ..
6 = 2x3
9 = 3x3
13 is prime, so LCM = 3x3x2x13 =234