a number is a common multiple of 7 and 11. It is the least such number with a sum of digits equal to 11. find the number
i think the answer is 10..but im not sure... can someone help pleasee???
To find the number which is the least common multiple of 7 and 11 and has a sum of digits equal to 11, we can use the following steps:
Step 1: Find the common multiples of 7 and 11.
- The common multiples of 7 and 11 are numbers that are divisible by both 7 and 11.
- Starting from 1, we can find the multiples of each number and check if they are common multiples.
- Multiples of 7: 7, 14, 21, 28, 35, 42, 49, ...
- Multiples of 11: 11, 22, 33, 44, 55, 66, 77, ...
Step 2: Identify the numbers with a sum of digits equal to 11.
- Among the common multiples, we need to identify the numbers whose digits add up to 11.
- To find this, we can calculate the sum of each number's digits until we find a number with a sum of 11.
Step 3: Find the least of these numbers.
- Finally, we need to find the least number from the list of numbers with a sum of digits equal to 11.
Let's apply these steps to find the number:
From the common multiples of 7 and 11, let's calculate the sum of digits for each number:
- For 7, the sum of digits is 7.
- For 14, the sum of digits is 1 + 4 = 5.
- For 21, the sum of digits is 2 + 1 = 3.
- For 28, the sum of digits is 2 + 8 = 10.
- For 35, the sum of digits is 3 + 5 = 8.
- For 42, the sum of digits is 4 + 2 = 6.
- For 49, the sum of digits is 4 + 9 = 13.
- For 55, the sum of digits is 5 + 5 = 10.
- For 66, the sum of digits is 6 + 6 = 12.
- For 77, the sum of digits is 7 + 7 = 14.
Among these numbers, the number with a sum of digits equal to 11 is 28.
Therefore, the least common multiple of 7 and 11 with a sum of digits equal to 11 is 28.