Formula of math What is the formula of LCM
Answers
\operatorname{lcm}(a,b)=\frac{|a \cdot b|}{\operatorname{gcd}(a,b)}
\operatorname{lcm}(a,b) = least common multiple of integers a and b
a = integer a
b = integer b
\operatorname{gcd}(a,b) = greatest common divisor of integers a and b
Step-by-step explanation:
LCM = \frac{a × b}{(gcd)(a,b)}
(gcd)(a,b)
a×b
2) To get the LCM of two Fractions, then first we need to compute the LCM of Numerators and HCF of the Denominators. Further, both these results will be expressed as a fraction. Thus,
LCM = \frac{L.C.M\;of\;Numerator}{H.C.F\;of\;Denominator}
H.C.FofDenominator
L.C.MofNumerator
Search for a topic
Home > Formulas > Maths Formulas > LCM Formula
Maths Formulas
LCM Formula
In mathematics computation of the least common multiple and greatest common divisors of two or more numbers. LCM is the smallest integer which is a multiple of two or more numbers. For example, LCM of 4 and 6 is 12, and LCM of 10 and 15 is 30. As with the greatest common divisors, there are many methods for computing the least common multiples also. One method is to factor both numbers into their primes. The LCM is the product of all primes that are common to all numbers. In this topic, we will discuss the concept of least common multiple and LCM formula with examples. Let us learn it!
Solve
Questions
Find the greatest common factor of the term in the following expression.
5a^4+10a^3-15a^25a
4
+10a
3
−15a
2
.
1 Verified answer
Find the H.C.F.H.C.F. of the expressions {x^3} + \left( {a + b} \right){x^2} + \left( {ab + 1} \right)x + bx
3
+(a+b)x
2
+(ab+1)x+b and {x^3} + 2a{x^2} + \left( {{a^2} + 1} \right)x + ax
3
+2ax
2
+(a
2
+1)x+a.
1 Verified answer
Find the highest common factors of the given terms:3x^2 y^3, 10x^3 y^2,6 x^2 y^2z3x
2
y
3
,10x
3
y
2
,6x
2
y
2
z
1 Verified answer
VIEW MORE
LCM Formula
What is LCM?
The Least Common Multiple i.e. LCM of two integers a and b is that smallest positive integer which is divisible by both a and b. Thus the smallest positive number is a multiple of two or more numbers.
For example, to calculate lcm of (40, 45), we will find factors of 40 and 45, getting
40 is expressed as 2× 2 × 2 × 5
45 is expressed as 3 × 3 × 5
The prime factors common to one or the other are 2, 2, 2, 3, 3, 5.
Thus the least common multiple will be 2 × 2 × 2 × 3 × 3 × 5 = 360.
Quick summary
with stories
LCM of Polynomials
2 mins read
HCF of Polynomials
2 mins read
To find out LCM using prime factorization method:
Step 1: Show each number as a product of their prime factors.
Step 2: LCM will be the product of the highest powers of all prime factors.
To find out the LCM using division Method:
Step 1: First, we need to write the given numbers in a horizontal line separated by commas.
Step 2: Then, we need to divide all the given numbers by the smallest prime number.
Step 3: We now need to write the quotients and undivided numbers in a new line below the previous one.
Step 4: Repeat this process until we find a stage where no prime factor is common.
Step 5: LCM will be the product of all the divisors and the numbers in the last line.
L.C.M formula for any two numbers:
1) For two given numbers if we know their greatest common divisor i.e. GCD, then LCM can be calculated easily with the help of given formula:
LCM = \frac{a × b}{(gcd)(a,b)}
(gcd)(a,b)
a×b
2) To get the LCM of two Fractions, then first we need to compute the LCM of Numerators and HCF of the Denominators. Further, both these results will be expressed as a fraction. Thus,
LCM = \frac{L.C.M\;of\;Numerator}{H.C.F\;of\;Denominator}
H.C.FofDenominator
L.C.MofNumerator
Solved Examples
Q.1: Find out the LCM of 8 and 14.
Solution:
Step 1: First write down each number as a product of prime factors.
8 = 2× 2 × 2 = 2³
14 = 2 × 7
Step 2: Product of highest powers of all prime factors.
Here the prime factors are 2 and 7
The highest power of 2 here = 2³
The highest power of 7 here = 7
Hence LCM = 2³ × 7 = 56
Q.2: If two numbers 12 and 30 are given. HCF of these two is 6 then find their LCM.
Solution: We will use the simple formula of LCM and GCD.
a = 12
b =30
gcd =6
Thus
LCM = \frac{a\times b}{gcd\left(a,b\right)}
gcd(a,b)
a×b
LCM = \frac {12 \times 30 } {6}
6
12×30
= 60
Step-by-step explanation:
The Least Common Multiple (LCM) 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. In simple words, the smallest positive number that is a multiple of two or more numbers is the LCM of those two numbers. Check out the LCM formula for any two numbers and for fractions using GCD (HCF) in the table given below.
I hope it will help u