The least three-digit number that is divisible by both 5 and 9 is 135.
If a number is divisible by both 2 and 3, it is also divisible by 6. This is because 6 is the least common multiple of 2 and 3. Therefore, any number that meets the criteria of being divisible by both 2 and 3 will also be divisible by 6.
A number that is both divisible by 32 and 36 can be found by calculating the least common multiple (LCM) of the two numbers. The LCM of 32 and 36 is 288. Therefore, 288 is a number that is divisible by both 32 and 36.
True. A number that is divisible by both 3 and 4 is also divisible by their least common multiple, which is 12. Since 12 can be expressed as (3 \times 4), any number meeting the criteria of being divisible by both 3 and 4 will indeed be divisible by 12.
To find a number that is divisible by both 2458 and 10, we need to find the least common multiple (LCM) of the two numbers. The LCM of 2458 and 10 is the smallest number that is a multiple of both 2458 and 10, which is 24580. Therefore, 24580 is the number that is divisible by both 2458 and 10.
110 is the smallest number divisible by both 10 and 11.
A number that is divisible by both 5 and 9 must be a multiple of their least common multiple (LCM). The LCM of 5 and 9 is 45. Therefore, any multiple of 45, such as 45, 90, or 135, will be divisible by both 5 and 9.
Any number that is divisible by both 2 and 3 is divisible by 6.
A three-digit number that is divisible by both three and four must also be divisible by their least common multiple, which is twelve. The smallest three-digit number divisible by twelve is 108, and the largest is 996. Therefore, any three-digit number that is a multiple of twelve, such as 120, 144, or 480, will meet the criteria of being divisible by both three and four.
To determine which number is divisible by both 9 and 4, we need to check if the number is divisible by both 9 and 4 simultaneously. A number is divisible by 9 if the sum of its digits is divisible by 9. A number is divisible by 4 if the number formed by its last two digits is divisible by 4. Among the options provided, only option D, 9126, meets both criteria as the sum of its digits is 18 (divisible by 9) and the number formed by its last two digits is 26 (divisible by 4).
If a number is divisible by both 8 and 11, it will be divisible by 88.
The smallest even number that is divisible by both 3 and 5 is 30. This is because the least common multiple (LCM) of 3 and 5 is 15, and the smallest even multiple of 15 is 30. Therefore, 30 meets the criteria of being both even and divisible by both 3 and 5.
A number that is divisible by both 8 and 9 must be a multiple of the least common multiple of 8 and 9, which is 72. Therefore, any number that is a multiple of 72 will be divisible by both 8 and 9. Examples of such numbers include 72, 144, 216, and so on.