i am three digits number.i am a common multiple of 3,7 and 11.the sum of my digits is 6.what number am i?what number am i if the sum of my digits is 18?
To find the three-digit number that is a common multiple of 3, 7, and 11 and has a sum of digits equal to 6, you can follow these steps:
1. Start by listing out the multiples of each number until you find a common multiple. For 3, the multiples are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150. For 7, the multiples are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147. For 11, the multiples are: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198.
2. Look for a common multiple among the numbers listed for each number. In this case, the number 77 is a common multiple of 3, 7, and 11.
3. Check if the sum of the digits of the number 77 is equal to 6. In this case, the sum of the digits of 77 is 7 + 7 = 14, which is not equal to 6.
Therefore, there is no three-digit number that is a common multiple of 3, 7, and 11 and has a sum of digits equal to 6.
To find the three-digit number that is a common multiple of 3, 7, and 11 and has a sum of digits equal to 18, you can follow similar steps:
1. List out the multiples of each number until you find a common multiple. For 3, the multiples are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150. For 7, the multiples are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147. For 11, the multiples are: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198.
2. Look for a common multiple among the numbers listed for each number. In this case, the number 693 is a common multiple of 3, 7, and 11.
3. Check if the sum of the digits of the number 693 is equal to 18. In this case, the sum of the digits of 693 is 6 + 9 + 3 = 18.
Therefore, the three-digit number that is a common multiple of 3, 7, and 11 and has a sum of digits equal to 18 is 693.
3*7*11 = 231
and 2+3+1 = 6
so that does it, 231
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three times that would have a sum of 18
so
3*231 = 693