the hundreds digit of the smallest six digit number divisible by 12, 13, 14, 15 and 16 is
the LCM is the smallest number divisible by all.
To get a 6-digit number,
100000/21840 = 4.57
so the smallest 6-digit number is
5*21840 = 109200
I'm sure you know how to find the hundreds digit in that
LCM(12,13,14,15,16) = 21840
its not the lcm, its the smallest six digit number and then what the hundreds place value is
To find the smallest six-digit number divisible by multiple numbers, we need to find the least common multiple (LCM) of those numbers. In this case, we want to find the LCM of 12, 13, 14, 15, and 16.
1. Start by listing the prime factors of each number:
- 12 = 2 * 2 * 3
- 13 is a prime number
- 14 = 2 * 7
- 15 = 3 * 5
- 16 = 2 * 2 * 2 * 2
2. Identify the highest power of each prime factor that appears in any of the numbers:
- 2 appears four times (2 * 2 * 2 * 2)
- 3 appears once
- 5 appears once
- 7 appears once
- 13 appears once
3. Multiply these prime factors with their highest powers to find the LCM:
LCM = 2 * 2 * 2 * 2 * 3 * 5 * 7 * 13
Upon multiplying these prime factors, we get LCM = 21840.
Now, we need to find the smallest six-digit number divisible by 21840. The smallest six-digit number is 100,000. We want to determine the hundreds digit of this number.
To do that, we divide 100,000 by 21840 and look at the remainder. If the remainder is zero, then the hundreds digit is zero. Otherwise, we divide the remainder by 1000 to get the hundreds digit.
Performing the division: 100,000 ÷ 21840 = 4 remainder 3200
Since the remainder is not zero, we divide 3200 by 1000 to get the hundreds digit.
Performing the division: 3200 ÷ 1000 = 3 remainder 200
Therefore, the hundreds digit of the smallest six-digit number divisible by 12, 13, 14, 15, and 16 is 3.