LCM Problems Quiz

What is the LCM of 98, 28 and 112 ?

• 784

• 1176

• 392

• 1568

Answer explanation

To find the LCM of 98, 28, and 112, we can use their prime factorizations: 98 = 2 x 7^2, 28 = 2^2 x 7, and 112 = 2^4 x 7. The LCM takes the highest powers: 2^4 and 7^2, resulting in 16 x 49 = 784.

The LCM of the numbers 36, 54, 72 and 96 is :

• 1064

• 764

• 864

• 964

Answer explanation

To find the LCM of 36, 54, 72, and 96, we determine the prime factorization of each number. The LCM is the product of the highest powers of all prime factors. This results in 864, which is the correct answer.

The LCM of the numbers 24, 42 and 56 is :

• 816

• 186

• 168

• 618

Answer explanation

To find the LCM of 24, 42, and 56, we first find their prime factorizations: 24 = 2^3 * 3, 42 = 2 * 3 * 7, and 56 = 2^3 * 7. The LCM is obtained by taking the highest power of each prime: 2^3, 3^1, and 7^1. Thus, LCM = 2^3 * 3^1 * 7^1 = 168.

The LCM of the numbers 70, 28 and 42 is :

• 116

• 420

• 280

• 700

Answer explanation

To find the LCM of 70, 28, and 42, we can use their prime factorizations: 70 = 2 × 5 × 7, 28 = 2^2 × 7, and 42 = 2 × 3 × 7. The LCM is found by taking the highest power of each prime: 2^2, 3^1, 5^1, 7^1. Thus, LCM = 4 × 3 × 5 × 7 = 420.

A Former plants three different types of plants in equal number in a garden. All plants of one type are planted to form a rectangle, in which no rectangle contains more than one type no plants of any type are left out. After all the plants were planted, the rectangle of plant A had 70 rows, the rectangle of plant B had 28 rows and the rectangle of plant C had 42 rows. Find the minimum number of plants of each type planted by the farmer in the garden.

• 70

• 420

• 210

• 140

Answer explanation

To find the minimum number of plants, calculate the least common multiple (LCM) of the rows: LCM(70, 28, 42) = 420. Thus, the minimum number of plants of each type is 420.

The LCM of two prime numbers x and y (x > y) is 119. The value of 3y – x is:

• 2

• 4

• 8

• 6

Answer explanation

The prime factors of 119 are 7 and 17. Since x > y, let x = 17 and y = 7. Then, 3y - x = 3(7) - 17 = 21 - 17 = 4. Thus, the answer is 4.

The L.C.M. of any two consecutive positive integers x and x + 1 is?

• 1

• (x)(x + 1)

• x

• x + 1

Answer explanation

The L.C.M. of two consecutive integers x and x + 1 is their product, (x)(x + 1), since they have no common factors other than 1. Thus, the correct answer is (x)(x + 1).

If the product of two co-primes is 104, then their LCM is?

• can't be determined

• is 104

• is 1

• is equal to their HCF

Answer explanation

For two co-prime numbers, their LCM is equal to their product. Since the product is 104, the LCM is also 104.

The LCM of 6, 9 and x is 72. Which of the given options can be a possible value of x?

• 18

• 12

• 36

• 24

Answer explanation

To find x, we need LCM(6, 9, x) = 72. The LCM of 6 and 9 is 18. For LCM(18, x) to be 72, x must be a multiple of 72/18 = 4. The only option that satisfies this is 24 (4 x 6). Thus, x can be 24.

What is the LCM of 22, 24, 48 and 16?

• 48

• 528

• 64

• 176

Answer explanation

To find the LCM of 22, 24, 48, and 16, we determine the highest powers of all prime factors: 2^4 (from 16), 3^1 (from 24), and 11^1 (from 22). Thus, LCM = 2^4 * 3^1 * 11^1 = 528, making 528 the correct answer.