lcm (66,924; 267,696) = ?
Approach 1. Integer numbers divisibility:
Divide the larger number by the smaller one.
Notice that dividing our numbers leaves no remainder:
267,696 ÷ 66,924 = 4 + 0;
=> 267,696 = 66,924 × 4;
So, 267,696 is divisible by 66,924.
267,696 is a multiple of 66,924.
The smallest multiple of 267,696 is the number itself: 267,696.
Consequently, least common multiple:
lcm (66,924; 267,696) = 267,696;
lcm (66,924; 267,696) = 267,696 = 24 × 32 × 11 × 132;
267,696 is a multiple of 66,924
Approach 2. Integer numbers prime factorization:
Prime Factorization of a number: finding the prime numbers that multiply together to make that number.
66,924 = 22 × 32 × 11 × 132;
66,924 is not a prime, is a composite number;
267,696 = 24 × 32 × 11 × 132;
267,696 is not a prime, is a composite number;
* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.
Calculate the least common multiple, lcm:
Multiply all the prime factors, by the largest exponents (if any).
lcm (66,924; 267,696) = 24 × 32 × 11 × 132;
lcm (66,924; 267,696) = 24 × 32 × 11 × 132 = 267,696
267,696 has all the prime factors of the number 66,924
Final answer:
Least common multiple
lcm (66,924; 267,696) = 267,696 = 24 × 32 × 11 × 132
267,696 is divisible by 66,924. 267,696 is a multiple of 66,924.
267,696 has all the prime factors of the number 66,924
Why do we need the least common multiple?
In order to add, subtract or compare fractions you have to first build their denominators the same. This common denominator is nothing else than the least common multiple of fractions' denominators, also called the least common denominator, lcd.
By definition, the least common multiple of two integers, LCM, is the smallest positive integer larger than 0 that is a multiple of both.
More operations of this kind:
Online calculator: LCM, the least common multiple
Tutoring: what is it and how to calculate the least common multiple LCM of integer numbers
60 is a common multiple of the numbers 6 and 15, because 60 is a multiple of 6 and is also a multiple of 15. But there is also an infinite number of common multiples of 6 and 15.
If "v" is a multiple of "a" and "b", then all the multiples of "v" are also multiples of "a" and "b".
Common multiples of 6 and 15 are: 30, 60, 90, 120... Among them, 30 is the lowest and we say that 30 is the least common multiple, or the lowest common multiple, or the smallest common multiple of 6 and 15, abbreviated as LCM.
If e = LCM (a; b), then "e" contains all the prime factors involved in the prime factorizations of both "a" and "b", by the highest powers (exponents).
Based on this rule we can calculate the least common multiple, LCM, of the three numbers in the example below:
- 40 = 23 × 5
- 36 = 22 × 32
- 126 = 2 × 32 × 7
- LCM (40; 36; 126) = 23 × 32 × 5 × 7 = 2,520