LCM of 7 and 12
LCM of 7 and 12 is the smallest number among all common multiples of 7 and 12. The first few multiples of 7 and 12 are (7, 14, 21, 28, . . . ) and (12, 24, 36, 48, 60, 72, 84, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 12  by listing multiples, by division method, and by prime factorization.
1.  LCM of 7 and 12 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 7 and 12?
Answer: LCM of 7 and 12 is 84.
Explanation:
The LCM of two nonzero integers, x(7) and y(12), is the smallest positive integer m(84) that is divisible by both x(7) and y(12) without any remainder.
Methods to Find LCM of 7 and 12
Let's look at the different methods for finding the LCM of 7 and 12.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 7 and 12 by Division Method
To calculate the LCM of 7 and 12 by the division method, we will divide the numbers(7, 12) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 12.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 7 and 12. Write this prime number(2) on the left of the given numbers(7 and 12), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (7, 12) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
 Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 7 and 12 is the product of all prime numbers on the left, i.e. LCM(7, 12) by division method = 2 × 2 × 3 × 7 = 84.
LCM of 7 and 12 by Prime Factorization
Prime factorization of 7 and 12 is (7) = 7^{1} and (2 × 2 × 3) = 2^{2} × 3^{1} respectively. LCM of 7 and 12 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{1} × 7^{1} = 84.
Hence, the LCM of 7 and 12 by prime factorization is 84.
LCM of 7 and 12 by Listing Multiples
To calculate the LCM of 7 and 12 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 7 (7, 14, 21, 28, . . . ) and 12 (12, 24, 36, 48, 60, 72, 84, . . . . )
 Step 2: The common multiples from the multiples of 7 and 12 are 84, 168, . . .
 Step 3: The smallest common multiple of 7 and 12 is 84.
∴ The least common multiple of 7 and 12 = 84.
☛ Also Check:
 LCM of 12 and 36  36
 LCM of 15 and 40  120
 LCM of 9 and 33  99
 LCM of 35 and 49  245
 LCM of 20 and 24  120
 LCM of 87 and 145  435
 LCM of 27 and 36  108
LCM of 7 and 12 Examples

Example 1: Verify the relationship between GCF and LCM of 7 and 12.
Solution:
The relation between GCF and LCM of 7 and 12 is given as,
LCM(7, 12) × GCF(7, 12) = Product of 7, 12
Prime factorization of 7 and 12 is given as, 7 = (7) = 7^{1} and 12 = (2 × 2 × 3) = 2^{2} × 3^{1}
LCM(7, 12) = 84
GCF(7, 12) = 1
LHS = LCM(7, 12) × GCF(7, 12) = 84 × 1 = 84
RHS = Product of 7, 12 = 7 × 12 = 84
⇒ LHS = RHS = 84
Hence, verified. 
Example 2: The GCD and LCM of two numbers are 1 and 84 respectively. If one number is 12, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 12 × a
⇒ a = (GCD × LCM)/12
⇒ a = (1 × 84)/12
⇒ a = 7
Therefore, the other number is 7. 
Example 3: The product of two numbers is 84. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 84
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 84/1
Therefore, the LCM is 84.
The probable combination for the given case is LCM(7, 12) = 84.
FAQs on LCM of 7 and 12
What is the LCM of 7 and 12?
The LCM of 7 and 12 is 84. To find the least common multiple (LCM) of 7 and 12, we need to find the multiples of 7 and 12 (multiples of 7 = 7, 14, 21, 28 . . . . 84; multiples of 12 = 12, 24, 36, 48 . . . . 84) and choose the smallest multiple that is exactly divisible by 7 and 12, i.e., 84.
How to Find the LCM of 7 and 12 by Prime Factorization?
To find the LCM of 7 and 12 using prime factorization, we will find the prime factors, (7 = 7) and (12 = 2 × 2 × 3). LCM of 7 and 12 is the product of prime factors raised to their respective highest exponent among the numbers 7 and 12.
⇒ LCM of 7, 12 = 2^{2} × 3^{1} × 7^{1} = 84.
What is the Relation Between GCF and LCM of 7, 12?
The following equation can be used to express the relation between GCF and LCM of 7 and 12, i.e. GCF × LCM = 7 × 12.
Which of the following is the LCM of 7 and 12? 21, 12, 84, 42
The value of LCM of 7, 12 is the smallest common multiple of 7 and 12. The number satisfying the given condition is 84.
If the LCM of 12 and 7 is 84, Find its GCF.
LCM(12, 7) × GCF(12, 7) = 12 × 7
Since the LCM of 12 and 7 = 84
⇒ 84 × GCF(12, 7) = 84
Therefore, the GCF = 84/84 = 1.
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