what is x if the lcm of 4,5,x is 60?Please show the formula or steps.TQ?

When finding the LCM of a set of numbers, find the prime factorization and then for each common base, collect the maximum exponent of that base, find the product, and that's your LCM.

Since we're given then LCM and need to find one of the three numbers, we have to work backwards a little bit.

So we'll do the prime factorizations of what we do know.

60 = 2² * 3¹ * 5¹
-------------------------
4 = 2² * 3º * 5º
5 = 2º * 3º * 5¹

So we already have our maximum 2 exponent in the 4, and the maximum 5 exponent in the 5. The only thing we're missing is the maximum 3 exponent.
x = 2^? * 3¹ * 5^?

Note that the exponent of the 2 can still be 0, 1, or 2 and the maximum exponent on the 2 is still 2. Same with the 5, exept it can be 0 or 1.

So there's 6 possible values for x that will make this work:

2º * 3¹ * 5º = 3
2º * 3¹ * 5¹ = 15
2¹ * 3¹ * 5º = 6
2¹ * 3¹ * 5¹ = 30
2² * 3¹ * 5º = 12
2² * 3¹ * 5¹ = 60

Any one of the above 6 values for x will keep the LCM of 4, 5, and x equal to 60.

x = 3, 6, 12, 15, 30, 60

Because:
3 x 2 x 2 x 5 = 3 x 4 x 5 = 60
2 x 3 x 2 x 5 = 6 x 2 x 5 = 60
3 x 5 x 2 x 2 = 15 x 2 x 2 = 60
2 x 3 x 5 x 2 = 30 x 2 = 60
2 x 2 x 3 x 5 = 60

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