LCM of 6 and 7
LCM of 6 and 7 is the smallest number among all common multiples of 6 and 7. The first few multiples of 6 and 7 are (6, 12, 18, 24, 30, 36, . . . ) and (7, 14, 21, 28, 35, 42, 49, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 7  by division method, by prime factorization, and by listing multiples.
1.  LCM of 6 and 7 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 6 and 7?
Answer: LCM of 6 and 7 is 42.
Explanation:
The LCM of two nonzero integers, x(6) and y(7), is the smallest positive integer m(42) that is divisible by both x(6) and y(7) without any remainder.
Methods to Find LCM of 6 and 7
The methods to find the LCM of 6 and 7 are explained below.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 6 and 7 by Division Method
To calculate the LCM of 6 and 7 by the division method, we will divide the numbers(6, 7) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 7.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 7. Write this prime number(2) on the left of the given numbers(6 and 7), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (6, 7) 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 6 and 7 is the product of all prime numbers on the left, i.e. LCM(6, 7) by division method = 2 × 3 × 7 = 42.
LCM of 6 and 7 by Listing Multiples
To calculate the LCM of 6 and 7 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, 36, . . . ) and 7 (7, 14, 21, 28, 35, 42, 49, . . . . )
 Step 2: The common multiples from the multiples of 6 and 7 are 42, 84, . . .
 Step 3: The smallest common multiple of 6 and 7 is 42.
∴ The least common multiple of 6 and 7 = 42.
LCM of 6 and 7 by Prime Factorization
Prime factorization of 6 and 7 is (2 × 3) = 2^{1} × 3^{1} and (7) = 7^{1} respectively. LCM of 6 and 7 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{1} × 7^{1} = 42.
Hence, the LCM of 6 and 7 by prime factorization is 42.
☛ Also Check:
 LCM of 4 and 5  20
 LCM of 8, 16 and 24  48
 LCM of 5, 8 and 12  120
 LCM of 24, 30 and 40  120
 LCM of 10 and 11  110
 LCM of 36 and 48  144
 LCM of 60 and 90  180
LCM of 6 and 7 Examples

Example 1: Find the smallest number that is divisible by 6 and 7 exactly.
Solution:
The smallest number that is divisible by 6 and 7 exactly is their LCM.
⇒ Multiples of 6 and 7: Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, . . . .
 Multiples of 7 = 7, 14, 21, 28, 35, 42, . . . .
Therefore, the LCM of 6 and 7 is 42.

Example 2: Verify the relationship between GCF and LCM of 6 and 7.
Solution:
The relation between GCF and LCM of 6 and 7 is given as,
LCM(6, 7) × GCF(6, 7) = Product of 6, 7
Prime factorization of 6 and 7 is given as, 6 = (2 × 3) = 2^{1} × 3^{1} and 7 = (7) = 7^{1}
LCM(6, 7) = 42
GCF(6, 7) = 1
LHS = LCM(6, 7) × GCF(6, 7) = 42 × 1 = 42
RHS = Product of 6, 7 = 6 × 7 = 42
⇒ LHS = RHS = 42
Hence, verified. 
Example 3: The product of two numbers is 42. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 42
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 42/1
Therefore, the LCM is 42.
The probable combination for the given case is LCM(6, 7) = 42.
FAQs on LCM of 6 and 7
What is the LCM of 6 and 7?
The LCM of 6 and 7 is 42. To find the least common multiple of 6 and 7, we need to find the multiples of 6 and 7 (multiples of 6 = 6, 12, 18, 24 . . . . 42; multiples of 7 = 7, 14, 21, 28 . . . . 42) and choose the smallest multiple that is exactly divisible by 6 and 7, i.e., 42.
What are the Methods to Find LCM of 6 and 7?
The commonly used methods to find the LCM of 6 and 7 are:
 Listing Multiples
 Division Method
 Prime Factorization Method
How to Find the LCM of 6 and 7 by Prime Factorization?
To find the LCM of 6 and 7 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (7 = 7). LCM of 6 and 7 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 7.
⇒ LCM of 6, 7 = 2^{1} × 3^{1} × 7^{1} = 42.
What is the Relation Between GCF and LCM of 6, 7?
The following equation can be used to express the relation between GCF and LCM of 6 and 7, i.e. GCF × LCM = 6 × 7.
If the LCM of 7 and 6 is 42, Find its GCF.
LCM(7, 6) × GCF(7, 6) = 7 × 6
Since the LCM of 7 and 6 = 42
⇒ 42 × GCF(7, 6) = 42
Therefore, the GCF = 42/42 = 1.
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