Grade 5 maths questions and problems on Lowest Common Multiple (LCM) are presented along with answers and detailed step-by-step solutions. In the questions below, Lowest Common Multiple is written as LCM.
Questions and Step-by-Step Solutions
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Question 1: Find the first 4 multiples of each number.
A) 2 B) 3 C) 5 D) 7 E) 10► View Step-by-Step Solution
To find the multiples of a number, multiply the number by 1, 2, 3, and 4:
A) 2: \(2 \times 1 = 2\), \(2 \times 2 = 4\), \(2 \times 3 = 6\), \(2 \times 4 = 8 \implies \mathbf{2, 4, 6, 8}\)
B) 3: \(3 \times 1 = 3\), \(3 \times 2 = 6\), \(3 \times 3 = 9\), \(3 \times 4 = 12 \implies \mathbf{3, 6, 9, 12}\)
C) 5: \(5 \times 1 = 5\), \(5 \times 2 = 10\), \(5 \times 3 = 15\), \(5 \times 4 = 20 \implies \mathbf{5, 10, 15, 20}\)
D) 7: \(7 \times 1 = 7\), \(7 \times 2 = 14\), \(7 \times 3 = 21\), \(7 \times 4 = 28 \implies \mathbf{7, 14, 21, 28}\)
E) 10: \(10 \times 1 = 10\), \(10 \times 2 = 20\), \(10 \times 3 = 30\), \(10 \times 4 = 40 \implies \mathbf{10, 20, 30, 40}\) -
Question 2: Find the LCM of each pair of numbers.
A) 2, 5 B) 4, 5 C) 7, 5 D) 12, 6► View Step-by-Step Solution
A) Multiples of 2: 2, 4, 6, 8, \(\mathbf{10}\), ...
Multiples of 5: 5, \(\mathbf{10}\), 15, ...
LCM = 10
B) Multiples of 4: 4, 8, 12, 16, \(\mathbf{20}\), ...
Multiples of 5: 5, 10, 15, \(\mathbf{20}\), ...
LCM = 20
C) Multiples of 7: 7, 14, 21, 28, \(\mathbf{35}\), ...
Multiples of 5: 5, 10, 15, 20, 25, 30, \(\mathbf{35}\), ...
LCM = 35
D) Multiples of 12: \(\mathbf{12}\), 24, ...
Multiples of 6: 6, \(\mathbf{12}\), 18, ...
LCM = 12 -
Question 3: Find the LCM of each triplet of numbers.
A) 2, 3, 12 B) 4, 5, 20 C) 5, 6, 10 D) 3, 6, 7► View Step-by-Step Solution
A) Multiples of 12: \(\mathbf{12}\), 24, ...
Since 2 and 3 both divide evenly into 12, the LCM is 12.
B) Multiples of 20: \(\mathbf{20}\), 40, ...
Since 4 and 5 both divide evenly into 20, the LCM is 20.
C) Multiples of 10: 10, 20, \(\mathbf{30}\), 40, ...
Check with 5 and 6: 5 divides 30, and 6 divides 30. LCM = 30.
D) Multiples of 7: 7, 14, 21, 28, 35, \(\mathbf{42}\), ...
Check with 3 and 6: 3 divides 42, and 6 divides 42. LCM = 42. -
Question 4: Find two numbers smaller than 10 and have an LCM equal to 20.
► View Step-by-Step Solution
We look for two whole numbers less than 10 whose least common multiple is 20.
Factors of 20 are 1, 2, 4, 5, 10, 20.
Let's test 4 and 5: Multiples of 4 are 4, 8, 12, 16, 20. Multiples of 5 are 5, 10, 15, 20. Both are smaller than 10, and their LCM is 20.
Answer: (4, 5) -
Question 5: Find two numbers that have an LCM equal to 6 and their sum is equal to 9.
► View Step-by-Step Solution
Let the two numbers be \(a\) and \(b\). We know that \(a + b = 9\) and \(\text{LCM}(a, b) = 6\).
Possible pairs of numbers that add up to 9: (1, 8), (2, 7), (3, 6), (4, 5).
- \(\text{LCM}(1, 8) = 8\) (Incorrect)
- \(\text{LCM}(2, 7) = 14\) (Incorrect)
- \(\text{LCM}(3, 6) = 6\) (Correct)
Answer: (3, 6) -
Question 6: 3 balls rotate along a circular track. Ball A makes one full rotation in 6 seconds. Ball B makes 9 seconds and ball C makes 12 seconds. If the three balls start rotating from the same point and at the same time now, after how many seconds will they all be at the same point again?
► View Step-by-Step Solution
To find when all three balls meet again at the starting point, we need to find the LCM of their individual rotation times: 6, 9, and 12 seconds.
- Multiples of 6: 6, 12, 18, 24, 30, \(\mathbf{36}\), ...
- Multiples of 9: 9, 18, 27, \(\mathbf{36}\), ...
- Multiples of 12: 12, 24, \(\mathbf{36}\), ...
The LCM is 36.
Answer: 36 seconds -
Question 7: 3 bulbs are used to make a flashing game. Bulb A flashes every 5 seconds. Bulb B flashes every 10 seconds and bulb C flashes every 25 seconds. If the game is switched on now, in how many seconds will all three bulbs flash at the same time?
► View Step-by-Step Solution
To find when all three bulbs flash together, we need to find the LCM of 5, 10, and 25 seconds.
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, \(\mathbf{50}\), ...
- Multiples of 10: 10, 20, 30, 40, \(\mathbf{50}\), ...
- Multiples of 25: 25, \(\mathbf{50}\), 75, ...
The LCM is 50.
Answer: 50 seconds