least common multiple of 5 and 15
The least common multiple of 5 and 15 is 15.
least common multiple of 10 and 12
To find the least common multiple of 10 and 12, we can list out the multiples of each number and then find the smallest multiple that they have in common.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120...
The smallest multiple that 10 and 12 have in common is 60. Therefore, the least common multiple of 10 and 12 is 60.
least common multiple of 18
The least common multiple of 18 is 18, since 18 is the only multiple of 18 itself.
multiples of 2 and 6
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90...
The multiples that are common to both 2 and 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60...
multiples of 8
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120...
40 divided by 8
40 divided by 8 is equal to 5:
40 ÷ 8 = 5
least common multiple of 9 and 12
To find the least common multiple of 9 and 12, we can list out the multiples of each number and then find the smallest multiple that they have in common.
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120...
The smallest multiple that 9 and 12 have in common is 36. Therefore, the least common multiple of 9 and 12 is 36.
multiples of 3
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45...
multiples of 7
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105...
which pair of numbers have an least common multiple of 60?
OPTIONS: 2 and 12, 5 and 12, 6 and 12, 3 and 12
To find the least common multiple of the given pairs of numbers, we can use the following:
LCM(a, b) = (a x b) / GCD(a, b)
where LCM(a, b) is the least common multiple of a and b, and GCD(a, b) is the greatest common divisor of a and b.
1. LCM(2, 12) = (2 x 12) / GCD(2, 12) = 24 / 2 = 12
2. LCM(5, 12) = (5 x 12) / GCD(5, 12) = 60 / 1 = 60
3. LCM(6, 12) = (6 x 12) / GCD(6, 12) = 12 / 6 = 12
4. LCM(3, 12) = (3 x 12) / GCD(3, 12) = 12 / 3 = 4
The only pair that has a least common multiple of 60 is 5 and 12. Therefore, the answer is option (B) 5 and 12.
multiples of 5 and 12
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240...
The multiples of 5 and 12 that are common to both are 60, 120, 180, 240...
which pair of numbers have an least common multiple of 16?
OPTIONS: 4 and 16, 2 and 4, 4 and 8, 3 and 16
To find the least common multiple of the given pairs of numbers, we can use the following:
LCM(a, b) = (a x b) / GCD(a, b)
where LCM(a, b) is the least common multiple of a and b, and GCD(a, b) is the greatest common divisor of a and b.
1. LCM(4, 16) = (4 x 16) / GCD(4, 16) = 16 / 4 = 4
2. LCM(2, 4) = (2 x 4) / GCD(2, 4) = 8 / 2 = 4
3. LCM(4, 8) = (4 x 8) / GCD(4, 8) = 8 / 4 = 2
4. LCM(3, 16) = (3 x 16) / GCD(3, 16) = 16 / 1 = 16
The only pair that has a least common multiple of 16 is 3 and 16. Therefore, the answer is option (D) 3 and 16.
multiples of 3 and 16
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60...
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240...
The multiples of 3 and 16 that are common to both are 48, 96, 144, 192, 240...
multiples of 4 and 16
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60...
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240...
The multiples of 4 and 16 that are common to both are 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240...
every 6th customer at a flower shot receives a free rose, and every 9th customer receives a free lily. Which customer will be the first to receive a free rose and a free lily?
We need to find the first customer number that is a multiple of both 6 and 9.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120...
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180...
The first customer number that is a multiple of both 6 and 9 is 18. Therefore, the 18th customer will be the first to receive a free rose and a free lily.
I am just doing the last one.
"We need to find the first customer number that is a multiple of both 6 and 9."
My way: (much quicker)
6 = 2 * 3
9 = 3 * 3
so we need one two and 2 threes
? = 2 * 3 * 3 = 18