LCM of 10 and 35
LCM of 10 and 35 is the smallest number among all common multiples of 10 and 35. The first few multiples of 10 and 35 are (10, 20, 30, 40, 50, 60, 70, . . . ) and (35, 70, 105, 140, 175, 210, 245, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 35  by division method, by prime factorization, and by listing multiples.
1.  LCM of 10 and 35 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 10 and 35?
Answer: LCM of 10 and 35 is 70.
Explanation:
The LCM of two nonzero integers, x(10) and y(35), is the smallest positive integer m(70) that is divisible by both x(10) and y(35) without any remainder.
Methods to Find LCM of 10 and 35
The methods to find the LCM of 10 and 35 are explained below.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 10 and 35 by Listing Multiples
To calculate the LCM of 10 and 35 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 10 (10, 20, 30, 40, 50, 60, 70, . . . ) and 35 (35, 70, 105, 140, 175, 210, 245, . . . . )
 Step 2: The common multiples from the multiples of 10 and 35 are 70, 140, . . .
 Step 3: The smallest common multiple of 10 and 35 is 70.
∴ The least common multiple of 10 and 35 = 70.
LCM of 10 and 35 by Division Method
To calculate the LCM of 10 and 35 by the division method, we will divide the numbers(10, 35) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 35.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 35. Write this prime number(2) on the left of the given numbers(10 and 35), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (10, 35) 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 10 and 35 is the product of all prime numbers on the left, i.e. LCM(10, 35) by division method = 2 × 5 × 7 = 70.
LCM of 10 and 35 by Prime Factorization
Prime factorization of 10 and 35 is (2 × 5) = 2^{1} × 5^{1} and (5 × 7) = 5^{1} × 7^{1} respectively. LCM of 10 and 35 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 5^{1} × 7^{1} = 70.
Hence, the LCM of 10 and 35 by prime factorization is 70.
☛ Also Check:
 LCM of 50 and 48  1200
 LCM of 5 and 9  45
 LCM of 5 and 8  40
 LCM of 5 and 7  35
 LCM of 5 and 6  30
 LCM of 5 and 30  30
 LCM of 5 and 25  25
LCM of 10 and 35 Examples

Example 1: The product of two numbers is 350. If their GCD is 5, what is their LCM?
Solution:
Given: GCD = 5
product of numbers = 350
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 350/5
Therefore, the LCM is 70.
The probable combination for the given case is LCM(10, 35) = 70. 
Example 2: Find the smallest number that is divisible by 10 and 35 exactly.
Solution:
The smallest number that is divisible by 10 and 35 exactly is their LCM.
⇒ Multiples of 10 and 35: Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, . . . .
 Multiples of 35 = 35, 70, 105, 140, 175, 210, 245, . . . .
Therefore, the LCM of 10 and 35 is 70.

Example 3: Verify the relationship between GCF and LCM of 10 and 35.
Solution:
The relation between GCF and LCM of 10 and 35 is given as,
LCM(10, 35) × GCF(10, 35) = Product of 10, 35
Prime factorization of 10 and 35 is given as, 10 = (2 × 5) = 2^{1} × 5^{1} and 35 = (5 × 7) = 5^{1} × 7^{1}
LCM(10, 35) = 70
GCF(10, 35) = 5
LHS = LCM(10, 35) × GCF(10, 35) = 70 × 5 = 350
RHS = Product of 10, 35 = 10 × 35 = 350
⇒ LHS = RHS = 350
Hence, verified.
FAQs on LCM of 10 and 35
What is the LCM of 10 and 35?
The LCM of 10 and 35 is 70. To find the least common multiple of 10 and 35, we need to find the multiples of 10 and 35 (multiples of 10 = 10, 20, 30, 40 . . . . 70; multiples of 35 = 35, 70, 105, 140) and choose the smallest multiple that is exactly divisible by 10 and 35, i.e., 70.
What are the Methods to Find LCM of 10 and 35?
The commonly used methods to find the LCM of 10 and 35 are:
 Prime Factorization Method
 Listing Multiples
 Division Method
What is the Least Perfect Square Divisible by 10 and 35?
The least number divisible by 10 and 35 = LCM(10, 35)
LCM of 10 and 35 = 2 × 5 × 7 [Incomplete pair(s): 2, 5, 7]
⇒ Least perfect square divisible by each 10 and 35 = LCM(10, 35) × 2 × 5 × 7 = 4900 [Square root of 4900 = √4900 = ±70]
Therefore, 4900 is the required number.
If the LCM of 35 and 10 is 70, Find its GCF.
LCM(35, 10) × GCF(35, 10) = 35 × 10
Since the LCM of 35 and 10 = 70
⇒ 70 × GCF(35, 10) = 350
Therefore, the GCF (greatest common factor) = 350/70 = 5.
Which of the following is the LCM of 10 and 35? 45, 5, 70, 12
The value of LCM of 10, 35 is the smallest common multiple of 10 and 35. The number satisfying the given condition is 70.
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