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Here are some samples of LCM of Numbers calculations.
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According to arithmetic and number theory, the least common multiple, lowest common multiple or the smallest common multiple of two numbers a and b, usually indicated as LCM(p, q) is the smallest positive integer which is divisible by both of the numbers.
Because the division of integers by zero is undefined, this explanation has meaning only if a and b are both different from zero. LCM stands for Least Common Multiple. LCM is defined as the smallest common multiple between 2 or more numbers.
Co-primes are a pair of numbers whose common factor comprises only 1. Thus, the LCM of two co-primes is always the product of these co-prime numbers. The LCM of p and q where p and q are co-primes is p × q.
The LCM is the smallest number that a set of numbers is divided into. Still, it will be greater than at least one number(or often both) of the given numbers. Moreover, if a number is the factor of another number, then their LCM will be the greater number itself.
LCM formula for any two numbers and fractions are :
L.C.M formula for any two numbers,
L.C.M. = a×b / gcd(a, b)
LCM formula for Fractions
L.C.M. = LCM of Numerators / HCF of denominators
Keep in mind that the GCD or HCF is the greatest divisor which will be divisible by both numbers.
The product of the LCM number of natural numbers is equal to the product of that number. LCM of a prime number is equal to the product of the number.
The Least Common Multiple or LCM of numbers can be evaluated using several methods.
LCM by using Prime Factorization Method
With the help of the prime factorization method, we can easily find out the LCM of the given numbers. To evaluate the LCM of two numbers using the prime factorization method, use the steps given below:
LCM by Division Method
For finding the LCM by division method, you should divide the numbers by a common prime number. Later, these prime factors are used to evaluate the LCM of those numbers. For a better understanding of this method use the steps given below:
If the prime number in step 1 is not any factor of the number, then note down the number in the row below as it is.
Find the least common multiple or LCM of 60 and 90 using the prime factorization method.
The prime factorization of 60 and 90 are: 60 = 2 × 2 × 3 × 5 and
90 = 2 × 3 × 3 × 5
If we write these prime factors in their exponential form it will be illustrated as,
60 = 22 × 31 × 51 and
90 = 21 × 32 × 51
Now, let's calculate the product of only those factors that have the highest power among these.
That will be,
22 × 32 × 51 = 4 × 5 × 9 = 180
Thus, LCM of 60 and 90 = 180.
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Several methods which can help you in calculating LCM are prime factorization, division method and listing multiples method.
The Least Common Multiple for two numbers, that is evenly divisible by both 24 and 36 is 72.
The Least Common Multiple is the smallest integer which tends to be the multiple of any set of numbers. For example, LCM for 12 and 21 can be calculated using any of the above-explained methods, resulting in 84.