The least common multiple of two numbers is 60 and one of the other number is 7 less than the other number what are the numbers justify your answer
Let numbers be x and y where y is greater y-x=7-equ(1) 60/x-60/y=7-equ(2) simplify equ 2:60y-60x/xy=7 60(y-x)/xy=7-equ 3 subt equ1 in equ3:420=7xy 420=7x(7+x) divide both sds by 7:60=x(7+x) x^2+7x-60=0 x(x+12)-5(x+12)=0 x=+5 y=7+5=12
I don't now.
To find the numbers, let's break down the problem step by step:
Step 1: Let's assume the two numbers are x and y, where x is the larger number and y is the smaller number.
Step 2: We know that the least common multiple (LCM) of x and y is 60. The LCM is the smallest number that is divisible by both x and y.
Step 3: We are also given that "one of the numbers is 7 less than the other number." This can be expressed as an equation: x = y + 7.
Step 4: We need to find the values of x and y that satisfy both the LCM condition and the equation x = y + 7.
Step 5: To solve for x and y, we can use a trial and error approach. Since the LCM is 60, we need to find two numbers that have 60 as their LCM.
Step 6: Let's start with a possible combination. For example, let's assume x = 20 and y = 13. We can check if this combination satisfies both conditions.
Condition 1: LCM of 20 and 13 = 260 (not equal to 60)
Condition 2: x = 20, y = 13 => 20 = 13 + 7 (not satisfied)
Step 7: Since the first combination did not satisfy both conditions, let's try another combination. Let's assume x = 30 and y = 23.
Condition 1: LCM of 30 and 23 = 690 (not equal to 60)
Condition 2: x = 30, y = 23 => 30 = 23 + 7 (not satisfied)
Step 8: We continue this process until we find a combination that satisfies both conditions.
Let's simplify the equation x = y + 7:
y = x - 7 (we can use this equation to find values of y)
After trying different combinations, we find that the values x = 37 and y = 30 satisfy both conditions.
Condition 1: LCM of 37 and 30 = 1110 (not equal to 60)
Condition 2: x = 37, y = 30 => 37 = 30 + 7 (satisfied)
Therefore, the numbers are 37 and 30, and they satisfy the given conditions.