Question

What is the least common multiple of \[9,10\] and \[7\]?

Answer 1

Hint: In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b.

Complete step-by-step solution:
It is given that; the numbers are \[9,10\] and \[7\].
We have to find the least common multiple of \[9,10\] and \[7\].
At first, we will find the factors of \[9,10\] and \[7\].
The factors of \[9\] are \[1,3,9\].
The factors of \[10\] are \[1,2,5,10\].
The factors of \[7\] are \[1,7\].
So, the common factor of \[9,10\]and \[7\]is \[1\] .
Since the common factor of these given numbers is \[1\] then the least common multiple of \[9,10\] and \[7\] is \[9 \times 10 \times 7\].
Simplifying we get, the least common multiple of \[9,10\] and \[7\] is \[630\].
Hence, the least common multiple of \[9,10\] and \[7\] is \[630\].

Note: The abbreviation LCM stands for "Least Common Multiple". The least common multiple of a number is the smallest number that is the product of two or more numbers. The least common multiple can be calculated for two or more integers as well as two or more fractions. The least common multiple of two numbers is the lowest possible number that can be divisible by both numbers.
There is more than one method to find the LCM of two numbers. One of the quickest ways to find the LCM of two numbers is to use the prime factorization of each number and then the product of the least powers of the common prime factors will be the LCM of those numbers.