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To find the least common multiple (LCM) of a set of numbers, we need to determine the prime factors of each number. The numbers given are 2, 3, 4, 5, 6, 9, and 10. The prime factors of these numbers are 2, 3, 2^2, 5, 2 * 3, 3^2, and 2 * 5 respectively. To find the LCM, we need to take the highest power of each prime factor that appears in any of the numbers. Multiplying these highest powers together gives us the LCM, which in this case is 2^2 * 3^2 * 5 = 180. Therefore, the least number divisible by 2, 3, 4, 5, 6, 9, and 10 is 180.
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What is the least number that is divisible by 2?
2
What is a number divisible by 2 3 4 5 and 10?
A number that is divisible by 2, 3, 4, 5, and 10 must be divisible by the least common multiple of these numbers, which is 60. Therefore, any number that is a multiple of 60 will be divisible by 2, 3, 4, 5, and 10. This is because 60 is the smallest number that contains all the prime factors of 2, 3, 4, 5, and 10.
What are the greatest and least numbers between 900 and 1000 that are divisible by 10 5 and 2?
To find the greatest number between 900 and 1000 that is divisible by 10, 5, and 2, we need to find the least common multiple (LCM) of 10, 5, and 2, which is 10. So, we look for the highest multiple of 10 between 900 and 1000, which is 990. To find the least number between 900 and 1000 that is divisible by 10, 5, and 2, we can simply find the smallest multiple of 10 in that range, which is 900.
What is a number that is divisible by 2 3 5 6 9 but not by 10?
There are no numbers that satisfy this. If a number is divisible by both 2 and 5, then it must also be divisible by 10.
What is the smallest number divisible by 2 and 5?
The smallest number divisible by both 2 and 5 is their least common multiple (LCM), which is the smallest number that is a multiple of both 2 and 5. The LCM of 2 and 5 is the product of the two numbers divided by their greatest common divisor (GCD). The GCD of 2 and 5 is 1, so the LCM is 2 * 5 / 1 = 10. Therefore, the smallest number divisible by both 2 and 5 is 10.
