A number is divisible by both 5 and 12. By which other number will that number be always divisible?

If a number is divisible by both 5 and 12, it is also divisible by their least common multiple (LCM). To find the LCM, we first consider the prime factorization of both numbers.

The number 5 is a prime number, so its factorization is simply 5 itself. The number 12 can be factored into primes as follows:

• 12 = 2 × 2 × 3 = 2² × 3

To find the LCM, we take the highest power of each prime that appears in the factorizations:

• From 5: 5¹
• From 12: 2² and 3¹

This gives us:

• LCM = 2² × 3¹ × 5¹ = 4 × 3 × 5 = 60

Therefore, any number that is divisible by both 5 and 12 will also be divisible by 60. In conclusion, the number that a number divisible by both 5 and 12 will always be divisible by is 60.