LCM of 34 and 51

LCM of 34 and 51 is the smallest number among all common multiples of 34 and 51. The first few multiples of 34 and 51 are (34, 68, 102, 136, 170, 204, 238, . . . ) and (51, 102, 153, 204, 255, 306, 357, . . . ) respectively. There are 3 commonly used methods to find LCM of 34 and 51 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 34 and 51 is 102.

Explanation:

The LCM of two non-zero integers, x(34) and y(51), is the smallest positive integer m(102) that is divisible by both x(34) and y(51) without any remainder.

The methods to find the LCM of 34 and 51 are explained below.

• By Listing Multiples
• By Division Method
• By Prime Factorization Method

LCM of 34 and 51 by Listing Multiples

To calculate the LCM of 34 and 51 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 34 (34, 68, 102, 136, 170, 204, 238, . . . ) and 51 (51, 102, 153, 204, 255, 306, 357, . . . . )
• Step 2: The common multiples from the multiples of 34 and 51 are 102, 204, . . .
• Step 3: The smallest common multiple of 34 and 51 is 102.

∴ The least common multiple of 34 and 51 = 102.

LCM of 34 and 51 by Division Method

To calculate the LCM of 34 and 51 by the division method, we will divide the numbers(34, 51) by their prime factors (preferably common). The product of these divisors gives the LCM of 34 and 51.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 34 and 51. Write this prime number(2) on the left of the given numbers(34 and 51), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (34, 51) 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 34 and 51 is the product of all prime numbers on the left, i.e. LCM(34, 51) by division method = 2 × 3 × 17 = 102.

LCM of 34 and 51 by Prime Factorization

Prime factorization of 34 and 51 is (2 × 17) = 2¹ × 17¹ and (3 × 17) = 3¹ × 17¹ respectively. LCM of 34 and 51 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 17¹ = 102.
Hence, the LCM of 34 and 51 by prime factorization is 102.

☛ Also Check:

• LCM of 7 and 56 - 56
• LCM of 13 and 17 - 221
• LCM of 7 and 14 - 14
• LCM of 4 and 5 - 20
• LCM of 10 and 100 - 100
• LCM of 12, 15 and 20 - 60
• LCM of 5, 10, 15 and 20 - 60

FAQs on LCM of 34 and 51

What is the LCM of 34 and 51?

The LCM of 34 and 51 is 102. To find the LCM of 34 and 51, we need to find the multiples of 34 and 51 (multiples of 34 = 34, 68, 102, 136; multiples of 51 = 51, 102, 153, 204) and choose the smallest multiple that is exactly divisible by 34 and 51, i.e., 102.

If the LCM of 51 and 34 is 102, Find its GCF.

LCM(51, 34) × GCF(51, 34) = 51 × 34
Since the LCM of 51 and 34 = 102
⇒ 102 × GCF(51, 34) = 1734
Therefore, the GCF (greatest common factor) = 1734/102 = 17.

What is the Relation Between GCF and LCM of 34, 51?

The following equation can be used to express the relation between GCF and LCM of 34 and 51, i.e. GCF × LCM = 34 × 51.

Which of the following is the LCM of 34 and 51? 2, 27, 102, 12

The value of LCM of 34, 51 is the smallest common multiple of 34 and 51. The number satisfying the given condition is 102.

How to Find the LCM of 34 and 51 by Prime Factorization?

To find the LCM of 34 and 51 using prime factorization, we will find the prime factors, (34 = 2 × 17) and (51 = 3 × 17). LCM of 34 and 51 is the product of prime factors raised to their respective highest exponent among the numbers 34 and 51.
⇒ LCM of 34, 51 = 2¹ × 3¹ × 17¹ = 102.